Question 1

$\text { Find the derivative of the function } f ( x ) = - 4 x ^ { 2 } - 4 \cos ( x ) \text {. }$

Accepted Answer

A)  $f ^ { t } ( x ) = - 4 x + 4 \sin ( x )$ 
B)  $f ^ {t } ( x ) = - 8 x + 4 \sin ( x )$ 
C)  $f ^ { t } ( x ) = - 8 x + 4 \cos ( x )$ 
D)  $f ^ { t} ( x ) = - 8 x - 4 \sin ( x )$ 
E)  $f ^ { t } ( x ) = - 8 x - 4 \cos ( x )$ 
A)  $f ^ { t } ( x ) = - 4 x + 4 \sin ( x )$ 
B)  $f ^ {t } ( x ) = - 8 x + 4 \sin ( x )$ 
C)  $f ^ { t } ( x ) = - 8 x + 4 \cos ( x )$ 
D)  $f ^ { t} ( x ) = - 8 x - 4 \sin ( x )$ 
E)  $f ^ { t } ( x ) = - 8 x - 4 \cos ( x )$

Question 2

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { 4 } + 7 x + 6 x y - y ^ { 7 } = 9$

Accepted Answer

A) $\frac { d y } { d x } = - \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$ 
B) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 - 6 y } { 7 y ^ { 6 } - 6 x }$ 
C) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 6 y ^ { 6 } - 6 x }$ 
D) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$ 
E) $\frac { d y } { d x } = \frac { 3 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$ 
A) $\frac { d y } { d x } = - \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$ 
B) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 - 6 y } { 7 y ^ { 6 } - 6 x }$ 
C) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 6 y ^ { 6 } - 6 x }$ 
D) $\frac { d y } { d x } = \frac { 4 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$ 
E) $\frac { d y } { d x } = \frac { 3 x ^ { 3 } + 7 + 6 y } { 7 y ^ { 6 } - 6 x }$

Question 3

$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$

Accepted Answer

A) $\frac { 16 x - 4 } { \left( 8 x ^ { 2 } - 4 x + 11 \right) ^ { 2 } }$ 
B)  $\frac { 16 x } { 8 x ^ { 2 } - 4 x + 11 }$ 
C)  $\frac { 16 x + 4 } { 8 x ^ { 2 } - 4 x + 11 }$ 
D)  $\frac { 16 x - 4 } { 8 x ^ { 2 } - 4 x + 11 }$ 
E)  $\frac { 1 } { 8 x ^ { 2 } - 4 x + 11 }$ 
A) $\frac { 16 x - 4 } { \left( 8 x ^ { 2 } - 4 x + 11 \right) ^ { 2 } }$ 
B)  $\frac { 16 x } { 8 x ^ { 2 } - 4 x + 11 }$ 
C)  $\frac { 16 x + 4 } { 8 x ^ { 2 } - 4 x + 11 }$ 
D)  $\frac { 16 x - 4 } { 8 x ^ { 2 } - 4 x + 11 }$ 
E)  $\frac { 1 } { 8 x ^ { 2 } - 4 x + 11 }$

Question 4

$\text { Evaluate } \frac { d y } { d x } \text { for the equation } x ^ { \frac { 4 } { 5 } } + y ^ { \frac { 4 } { 5 } } = 257 \text { at the given point } ( 1024,1 ) \text {. Round }$ your answer to two decimal places.

Accepted Answer

A)  $\frac { d y } { d x } = 16.00$ 
B)  $\frac { d y } { d x } = 4.00$ 
C)  $\frac { d y } { d x } = - 0.25$ 
D)  $\frac { d y } { d x } = 0.25$ 
E)  $\frac { d y } { d x } = - 0.06$ 
A)  $\frac { d y } { d x } = 16.00$ 
B)  $\frac { d y } { d x } = 4.00$ 
C)  $\frac { d y } { d x } = - 0.25$ 
D)  $\frac { d y } { d x } = 0.25$ 
E)  $\frac { d y } { d x } = - 0.06$

Question 5

$\text { Find } f ^ { t } ( t ) \text { if } f ( t ) = t ^ { 10 } 10 ^ { 7 t }$

Accepted Answer

A)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 70 t ^ { 10 } 10 ^ { 7 t }$ 
B)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 7 t ^ { 10 } 10 ^ { 7 t - 1 }$ 
C)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 7 \ln ( 10 ) t ^ { 10 } 10 ^ { 7 t }$ 
D)  $f ^ {t } ( t ) = 10 t ^ { 9 } 70 ^ { 7 t - 1 }$ 
E)  $f ^ { t} ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 10 ^ { 7 t - 1 }$ 
A)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 70 t ^ { 10 } 10 ^ { 7 t }$ 
B)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 7 t ^ { 10 } 10 ^ { 7 t - 1 }$ 
C)  $f ^ { t } ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 7 \ln ( 10 ) t ^ { 10 } 10 ^ { 7 t }$ 
D)  $f ^ {t } ( t ) = 10 t ^ { 9 } 70 ^ { 7 t - 1 }$ 
E)  $f ^ { t} ( t ) = 10 t ^ { 9 } 10 ^ { 7 t } + 10 ^ { 7 t - 1 }$

Question 6

$\text { Find the derivative of the function } f ( x ) = \frac { 2 } { \sqrt [ 3 ] { x } } + 3 \cos x \text {. }$

Accepted Answer

A)  $f ^ { t } ( x ) = \frac { 2 } { 3 x ^ { 4 / 3 } } - 3 \sin x$ 
B)  $f ^ {t} ( x ) = - \frac { 2 } { 3 x ^ { 4 / 3 } } - 3 \sin x$ 
C)  $f ^ { t} ( x ) = - \frac { 2 } { 3 x ^ { 4 / 3 } } + 3 \sin x$ 
D)  $f ^ { t } ( x ) = - \frac { 2 } { 3 x ^ { 3 / 4 } } - 3 \sin x$ 
E)  $f ^ { t } ( x ) = - \frac { 2 } { 3 x ^ { 3 / 4 } } + 3 \sin x$ 
A)  $f ^ { t } ( x ) = \frac { 2 } { 3 x ^ { 4 / 3 } } - 3 \sin x$ 
B)  $f ^ {t} ( x ) = - \frac { 2 } { 3 x ^ { 4 / 3 } } - 3 \sin x$ 
C)  $f ^ { t} ( x ) = - \frac { 2 } { 3 x ^ { 4 / 3 } } + 3 \sin x$ 
D)  $f ^ { t } ( x ) = - \frac { 2 } { 3 x ^ { 3 / 4 } } - 3 \sin x$ 
E)  $f ^ { t } ( x ) = - \frac { 2 } { 3 x ^ { 3 / 4 } } + 3 \sin x$

Question 7

$\text { Find the derivative of the function } f ( x ) = 6 e ^ { 8 x } - e ^ { - 4 x } \text {. }$

Accepted Answer

A)  $48 e ^ { 7 x } + 4 e ^ { - 5 x }$ 
B)  $8 e ^ { 8 x } - 4 e ^ { - 4 x }$ 
C)  $48 e ^ { 8 x } - 4 e ^ { - 4 x }$ 
D)  $8 e ^ { 8 x } + 4 e ^ { - 4 x }$ 
E)  $48 e ^ { 8 x } + 4 e ^ { - 4 x }$ 
A)  $48 e ^ { 7 x } + 4 e ^ { - 5 x }$ 
B)  $8 e ^ { 8 x } - 4 e ^ { - 4 x }$ 
C)  $48 e ^ { 8 x } - 4 e ^ { - 4 x }$ 
D)  $8 e ^ { 8 x } + 4 e ^ { - 4 x }$ 
E)  $48 e ^ { 8 x } + 4 e ^ { - 4 x }$

Question 8

$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$

Accepted Answer

A)  $\frac { 9 } { 2 } \sqrt { x } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
B)  $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
C)  $\frac { 9 } { 2 \sqrt { x } } \cos ( x )$ 
D)  $\frac { - 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
E)  $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) - 9 \sqrt { x } \cos ( x )$ 
A)  $\frac { 9 } { 2 } \sqrt { x } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
B)  $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
C)  $\frac { 9 } { 2 \sqrt { x } } \cos ( x )$ 
D)  $\frac { - 9 } { 2 \sqrt { x } } \sin ( x ) + 9 \sqrt { x } \cos ( x )$ 
E)  $\frac { 9 } { 2 \sqrt { x } } \sin ( x ) - 9 \sqrt { x } \cos ( x )$

Question 9

All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume changing when each edge is centimeters?

Accepted Answer

A)  $486 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
B)  $72 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
C)  $36 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
D)  $108 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
E)  $162 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
A)  $486 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
B)  $72 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
C)  $36 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
D)  $108 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$ 
E)  $162 \mathrm {~cm} ^ { 3 } / \mathrm { sec }$

Question 10

$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$

Accepted Answer

A)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } - 25 t ^ { 4 }$ 
B)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } + 36 t ^ { 4 }$ 
C)  $H ^ { t} ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } + 25 t ^ { 4 }$ 
D)  $H ^ {t } ( s ) = 11 t ^ { 10 } - 36 t ^ { 5 } - 25 t ^ { 4 }$ 
E)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } - 6 t ^ { 4 }$ 
A)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } - 25 t ^ { 4 }$ 
B)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } + 36 t ^ { 4 }$ 
C)  $H ^ { t} ( s ) = 11 t ^ { 10 } + 36 t ^ { 5 } + 25 t ^ { 4 }$ 
D)  $H ^ {t } ( s ) = 11 t ^ { 10 } - 36 t ^ { 5 } - 25 t ^ { 4 }$ 
E)  $H ^ { t } ( s ) = 11 t ^ { 10 } + 25 t ^ { 5 } - 6 t ^ { 4 }$

Question 11

$\text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { 8 x } { x ^ { 5 } + 3 } \text {. }$

Accepted Answer

A) $f ^ { t} ( x ) = - \frac { 8 \left( - 3 + 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
B) $f ^ { t } ( x ) = \frac { 8 \left( - 3 - 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
C) $f ^ { t } ( x ) = - \frac { 8 \left( 3 + 5 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
D) $f ^ { t } ( x ) = \frac { 8 \left( 3 + 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
E) $f ^ { t } ( x ) = - \frac { 8 \left( 3 + 6 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
A) $f ^ { t} ( x ) = - \frac { 8 \left( - 3 + 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
B) $f ^ { t } ( x ) = \frac { 8 \left( - 3 - 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
C) $f ^ { t } ( x ) = - \frac { 8 \left( 3 + 5 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
D) $f ^ { t } ( x ) = \frac { 8 \left( 3 + 4 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$ 
E) $f ^ { t } ( x ) = - \frac { 8 \left( 3 + 6 x ^ { 5 } \right) } { \left( x ^ { 5 } + 3 \right) ^ { 2 } }$

Question 12

$\text { Find the derivative of the function } f ( x ) = 9 \arcsin \left( 6 x ^ { 2 } + 19 x - 9 \right)$

Accepted Answer

A) $f ^ { t } ( x ) = \frac { 9 } { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } }$ 
B) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } }$ 
C) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { \sqrt { 1 - \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$ 
D) $f ^ { t} ( x ) = \frac { 9 } { \sqrt { 1 - \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$ 
E) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { \sqrt { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$ 
A) $f ^ { t } ( x ) = \frac { 9 } { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } }$ 
B) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } }$ 
C) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { \sqrt { 1 - \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$ 
D) $f ^ { t} ( x ) = \frac { 9 } { \sqrt { 1 - \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$ 
E) $f ^ { t } ( x ) = \frac { 9 ( 12 x + 19 ) } { \sqrt { 1 + \left( 6 x ^ { 2 } + 19 x - 9 \right) ^ { 2 } } }$

Question 13

Newton´s Method to approximate the x-value of the indicated point of intersection of the two graphs accurate to three decimal places.Continue the process until two Successive approximations differ by less tha $0.001 \text {. [Hint: Let } h ( x ) = f ( x ) - g ( x ) . ]$ $f ( x ) = 3 x + 1$
$g ( x ) = \sqrt { x + 5 }$

Accepted Answer

A) $0.444$ 
B)  $0.371$ 
C)  $0.432$ 
D)  $0.393$ 
E)  $0.476$ 
A) $0.444$ 
B)  $0.371$ 
C)  $0.432$ 
D)  $0.393$ 
E)  $0.476$

Question 14

a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time $t = 0$. At what time will the object reach the ground level?

Accepted Answer

A)  3 seconds 
B)  6 seconds 
C)  7 seconds 
D)  5 seconds 
E)  4 seconds 
A)  3 seconds 
B)  6 seconds 
C)  7 seconds 
D)  5 seconds 
E)  4 seconds

Question 15

Assume that x and y are both differentiable functions of t. Find $\frac { d x } { d t }$ when $x = 11$ and $\frac { d y } { d t } = - 8$ for the equation $x y = 132$.

Accepted Answer

A)  $\frac { d x } { d t } = - 1056$ 
B)  $\frac { d x } { d t } = 88$ 
C)  $\frac { d x } { d t } = - \frac { 22 } { 3 }$ 
D)  $\frac { d x } { d t } = \frac { 22 } { 3 }$ 
E)  $\frac { d x } { d t } = - 88$ 
A)  $\frac { d x } { d t } = - 1056$ 
B)  $\frac { d x } { d t } = 88$ 
C)  $\frac { d x } { d t } = - \frac { 22 } { 3 }$ 
D)  $\frac { d x } { d t } = \frac { 22 } { 3 }$ 
E)  $\frac { d x } { d t } = - 88$

Question 16

Find the derivative of the function. $y = \frac { 3 } { 5 } \sec ^ { 2 } x$

Accepted Answer

A)  $y ^ { t } = - \frac { 6 } { 5 } \sec ^ { 2 } x \tan x$ 
B)  $y ^ { t } = \frac { 6 } { 5 } \sec ^ { 2 } x \tan ^ { 2 } x$ 
C)  $y ^ {t } = \frac { 6 } { 5 } \sec x \tan x$ 
D)  $y ^ { t } = \frac { 6 } { 5 } \sec ^ { 2 } x \tan x$ 
E)  $y ^ { t } = \frac { 3 } { 5 } \sec ^ { 2 } x \tan x$ 
A)  $y ^ { t } = - \frac { 6 } { 5 } \sec ^ { 2 } x \tan x$ 
B)  $y ^ { t } = \frac { 6 } { 5 } \sec ^ { 2 } x \tan ^ { 2 } x$ 
C)  $y ^ {t } = \frac { 6 } { 5 } \sec x \tan x$ 
D)  $y ^ { t } = \frac { 6 } { 5 } \sec ^ { 2 } x \tan x$ 
E)  $y ^ { t } = \frac { 3 } { 5 } \sec ^ { 2 } x \tan x$

Question 17

$\text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. }$

Accepted Answer

A)  $f ^ { t } ( u ) = 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 7 } } { 2 \sqrt { u } }$ 
B)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
C)  $f ^ { t } ( u ) = 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
D)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
E)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
A)  $f ^ { t } ( u ) = 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 7 } } { 2 \sqrt { u } }$ 
B)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
C)  $f ^ { t } ( u ) = 6 u ^ { \frac { 13 } { 2 } } - \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
D)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 11 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$ 
E)  $f ^ { t } ( u ) = - 6 u ^ { \frac { 13 } { 2 } } + \frac { 5 - u ^ { 6 } } { 2 \sqrt { u } }$

Question 18

Find the derivative of the function. $f ( x ) = x ^ { 7 } ( 5 + 8 x ) ^ { 3 }$

Accepted Answer

A)  $f ^ {t } ( x ) = x ^ { 2 } ( 5 + 8 x ) ^ { 6 } ( 35 + 80 x )$ 
B)  $f ^ { t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 2 } ( 35 + 80 x )$ 
C)  $f ^ {t } ( x ) = 8 x ^ { 7 } ( 5 + 8 x ) ^ { 2 } ( 35 + 80 x )$ 
D)  $f ^ {t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 3 } ( 35 + 80 x )$ 
E)  $f ^ { t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 2 } ( 35 + 8 x )$ 
A)  $f ^ {t } ( x ) = x ^ { 2 } ( 5 + 8 x ) ^ { 6 } ( 35 + 80 x )$ 
B)  $f ^ { t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 2 } ( 35 + 80 x )$ 
C)  $f ^ {t } ( x ) = 8 x ^ { 7 } ( 5 + 8 x ) ^ { 2 } ( 35 + 80 x )$ 
D)  $f ^ {t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 3 } ( 35 + 80 x )$ 
E)  $f ^ { t } ( x ) = x ^ { 6 } ( 5 + 8 x ) ^ { 2 } ( 35 + 8 x )$

Question 19

$\text { Find the slope of the tangent line } ( 16 - x ) y ^ { 2 } = x ^ { 3 } \text { at the given point } ( 8,8 ) \text {. Round }$ your answer to two decimal places.

Accepted Answer

A) $0.67$ 
B)  $2.00$ 
C)  $1.00$ 
D)  $1.67$ 
E)  $3.00$ 
A) $0.67$ 
B)  $2.00$ 
C)  $1.00$ 
D)  $1.67$ 
E)  $3.00$

Question 20

$\text { Find the derivative of the function } f ( x ) = 4 e ^ { x } \cos ( x ) \text {. Simplify your answer. }$

Accepted Answer

A)  $4 e ^ { x } ( \cos ( x ) + \sin ( x ) )$ 
B)  $- 4 e ^ { x } \sin ( x )$ 
C)  $4 e ^ { x } \cos ( x )$ 
D)  $4 e ^ { x } \sin ( x ) \cos ( x )$ 
E)  $4 e ^ { x } ( \cos ( x ) - \sin ( x ) )$ 
A)  $4 e ^ { x } ( \cos ( x ) + \sin ( x ) )$ 
B)  $- 4 e ^ { x } \sin ( x )$ 
C)  $4 e ^ { x } \cos ( x )$ 
D)  $4 e ^ { x } \sin ( x ) \cos ( x )$ 
E)  $4 e ^ { x } ( \cos ( x ) - \sin ( x ) )$

$\text { Find the derivative of the function } f ( x ) = - 4 x ^ { 2 } - 4 \cos ( x ) \text {. }$

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { 4 } + 7 x + 6 x y - y ^ { 7 } = 9$

$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$

$\text { Evaluate } \frac { d y } { d x } \text { for the equation } x ^ { \frac { 4 } { 5 } } + y ^ { \frac { 4 } { 5 } } = 257 \text { at the given point } ( 1024,1 ) \text {. Round }$ your answer to two decimal places.

$\text { Find } f ^ { t } ( t ) \text { if } f ( t ) = t ^ { 10 } 10 ^ { 7 t }$

$\text { Find the derivative of the function } f ( x ) = \frac { 2 } { \sqrt [ 3 ] { x } } + 3 \cos x \text {. }$

$\text { Find the derivative of the function } f ( x ) = 6 e ^ { 8 x } - e ^ { - 4 x } \text {. }$

$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$

All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume changing when each edge is centimeters?

$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$

$\text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { 8 x } { x ^ { 5 } + 3 } \text {. }$

$\text { Find the derivative of the function } f ( x ) = 9 \arcsin \left( 6 x ^ { 2 } + 19 x - 9 \right)$

a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time $t = 0$ . At what time will the object reach the ground level?

Assume that x and y are both differentiable functions of t. Find $\frac { d x } { d t }$ when $x = 11$ and $\frac { d y } { d t } = - 8$ for the equation $x y = 132$ .

Find the derivative of the function. $y = \frac { 3 } { 5 } \sec ^ { 2 } x$

$\text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. }$

Find the derivative of the function. $f ( x ) = x ^ { 7 } ( 5 + 8 x ) ^ { 3 }$

$\text { Find the slope of the tangent line } ( 16 - x ) y ^ { 2 } = x ^ { 3 } \text { at the given point } ( 8,8 ) \text {. Round }$ your answer to two decimal places.

$\text { Find the derivative of the function } f ( x ) = 4 e ^ { x } \cos ( x ) \text {. Simplify your answer. }$

Graphs and Models

A Preview of Calculus

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 3: The Derivative and the Tangent Line Problem

Find the derivative of the function f(x)=−4x2−4cos⁡(x). \text { Find the derivative of the function } f ( x ) = - 4 x ^ { 2 } - 4 \cos ( x ) \text {. } Find the derivative of the function f(x)=−4x2−4cos(x).

Find dydx by implicit differentiation. \text { Find } \frac { d y } { d x } \text { by implicit differentiation. } Find dxdy​ by implicit differentiation. x4+7x+6xy−y7=9x ^ { 4 } + 7 x + 6 x y - y ^ { 7 } = 9x4+7x+6xy−y7=9

Differentiate the function f(x)=ln⁡(8x2−4x+11). \text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. } Differentiate the function f(x)=ln(8x2−4x+11).

Find ft(t) if f(t)=t10107t\text { Find } f ^ { t } ( t ) \text { if } f ( t ) = t ^ { 10 } 10 ^ { 7 t } Find ft(t) if f(t)=t10107t

Find the derivative of the function f(x)=2x3+3cos⁡x. \text { Find the derivative of the function } f ( x ) = \frac { 2 } { \sqrt [ 3 ] { x } } + 3 \cos x \text {. } Find the derivative of the function f(x)=3x​2​+3cosx.

Find the derivative of the function f(x)=6e8x−e−4x. \text { Find the derivative of the function } f ( x ) = 6 e ^ { 8 x } - e ^ { - 4 x } \text {. } Find the derivative of the function f(x)=6e8x−e−4x.

Find the derivative of the function f(x)=9xsin⁡(x). \text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. } Find the derivative of the function f(x)=9x​sin(x).

All edges of a cube are expanding at a rate of centimeters per second. How fast is the volume changing when each edge is centimeters?

Find the derivative of the algebraic function H(t)=(t6−5)(t5+6)\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right) Find the derivative of the algebraic function H(t)=(t6−5)(t5+6)

Use the Quotient Rule to differentiate the function f(x)=8xx5+3. \text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { 8 x } { x ^ { 5 } + 3 } \text {. } Use the Quotient Rule to differentiate the function f(x)=x5+38x​.

Find the derivative of the function f(x)=9arcsin⁡(6x2+19x−9)\text { Find the derivative of the function } f ( x ) = 9 \arcsin \left( 6 x ^ { 2 } + 19 x - 9 \right) Find the derivative of the function f(x)=9arcsin(6x2+19x−9)

a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time t=0t = 0t=0 . At what time will the object reach the ground level?

Assume that x and y are both differentiable functions of t. Find dxdt\frac { d x } { d t }dtdx​ when x=11x = 11x=11 and dydt=−8\frac { d y } { d t } = - 8dtdy​=−8 for the equation xy=132x y = 132xy=132 .

Find the derivative of the function. y=35sec⁡2xy = \frac { 3 } { 5 } \sec ^ { 2 } xy=53​sec2x

Use the Product Rule to differentiate f(u)=u(5−u6). \text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. } Use the Product Rule to differentiate f(u)=u​(5−u6).

Find the derivative of the function. f(x)=x7(5+8x)3f ( x ) = x ^ { 7 } ( 5 + 8 x ) ^ { 3 }f(x)=x7(5+8x)3

Find the derivative of the function f(x)=4excos⁡(x). Simplify your answer. \text { Find the derivative of the function } f ( x ) = 4 e ^ { x } \cos ( x ) \text {. Simplify your answer. } Find the derivative of the function f(x)=4excos(x). Simplify your answer.

Graphs and Models

A Preview of Calculus

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

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$\text { Find the derivative of the function } f ( x ) = - 4 x ^ { 2 } - 4 \cos ( x ) \text {. }$

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $x ^ { 4 } + 7 x + 6 x y - y ^ { 7 } = 9$

$\text { Differentiate the function } f ( x ) = \ln \left( 8 x ^ { 2 } - 4 x + 11 \right) \text {. }$

$\text { Find } f ^ { t } ( t ) \text { if } f ( t ) = t ^ { 10 } 10 ^ { 7 t }$

$\text { Find the derivative of the function } f ( x ) = \frac { 2 } { \sqrt [ 3 ] { x } } + 3 \cos x \text {. }$

$\text { Find the derivative of the function } f ( x ) = 6 e ^ { 8 x } - e ^ { - 4 x } \text {. }$

$\text { Find the derivative of the function } f ( x ) = 9 \sqrt { x } \sin ( x ) \text {. }$

$\text { Find the derivative of the algebraic function } H ( t ) = \left( t ^ { 6 } - 5 \right) \left( t ^ { 5 } + 6 \right)$

$\text { Use the Quotient Rule to differentiate the function } f ( x ) = \frac { 8 x } { x ^ { 5 } + 3 } \text {. }$

$\text { Find the derivative of the function } f ( x ) = 9 \arcsin \left( 6 x ^ { 2 } + 19 x - 9 \right)$

a free-fall experiment, an object is dropped from a height of 256 feet. A camera on the ground 500 feet from the point of impact records the fall of the object as shown in the figure. Assuming the object is released at time $t = 0$ . At what time will the object reach the ground level?

Assume that x and y are both differentiable functions of t. Find $\frac { d x } { d t }$ when $x = 11$ and $\frac { d y } { d t } = - 8$ for the equation $x y = 132$ .

Find the derivative of the function. $y = \frac { 3 } { 5 } \sec ^ { 2 } x$

$\text { Use the Product Rule to differentiate } f ( u ) = \sqrt { u } \left( 5 - u ^ { 6 } \right) \text {. }$

Find the derivative of the function. $f ( x ) = x ^ { 7 } ( 5 + 8 x ) ^ { 3 }$

$\text { Find the derivative of the function } f ( x ) = 4 e ^ { x } \cos ( x ) \text {. Simplify your answer. }$