Question 1

Compute the derivative.   $\frac { \mathrm { d } } { \mathrm { d } x } \left[ \left( x ^ { 3 } + 2 x \right) \left( x ^ { 2 } - x \right) \right] _ { x = - 2 }$

Accepted Answer

A) -108 
B)  132 
C)  100 
D)  131 
E)  144 
A) -108 
B)  132 
C)  100 
D)  131 
E)  144

Question 2

Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ using implicit differentiation.   $\frac { e ^ { x } } { y ^ { 2 } } = 16 + e ^ { y }$

Accepted Answer

A)  $\frac { y e ^ { x } } { 16 e ^ { x } + 3 y ^ { 2 } e ^ { y } }$ 
B)    $\frac { 2 y e ^ { x } } { e ^ { x } + y e ^ { y } }$ 
C)    $\frac { 2 e ^ { x } + y ^ { 3 } e ^ { y } } { y e ^ { x } }$ 
D)    $\frac { y e ^ { x } } { 2 e ^ { x } + y ^ { 3 } e ^ { y } }$ 
E)    $\frac { y } { 2 + y ^ { 3 } }$ 
A)  $\frac { y e ^ { x } } { 16 e ^ { x } + 3 y ^ { 2 } e ^ { y } }$ 
B)    $\frac { 2 y e ^ { x } } { e ^ { x } + y e ^ { y } }$ 
C)    $\frac { 2 e ^ { x } + y ^ { 3 } e ^ { y } } { y e ^ { x } }$ 
D)    $\frac { y e ^ { x } } { 2 e ^ { x } + y ^ { 3 } e ^ { y } }$ 
E)    $\frac { y } { 2 + y ^ { 3 } }$

Question 3

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer.  $y = \frac { 2 x + 2 } { 4 x - 5 }$

Accepted Answer

A)  $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { 4 x - 5 }$ 
B)  $\frac { 2 ( 4 x - 5 ) - 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$ 
C)  $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$ 
D)  $2 ( 4 x - 5 ) - 4 ( 2 x + 2 )$ 
E)  0.5 
A)  $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { 4 x - 5 }$ 
B)  $\frac { 2 ( 4 x - 5 ) - 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$ 
C)  $\frac { 2 ( 4 x - 5 ) + 4 ( 2 x + 2 ) } { ( 4 x - 5 ) ^ { 2 } }$ 
D)  $2 ( 4 x - 5 ) - 4 ( 2 x + 2 )$ 
E)  0.5

Question 4

The number P of CDs the Snappy Hardware Co. can manufacture at its plant in one day is given by
​ $P = x ^ { 0.7 } y ^ { 0.6 }$ ​
where x is the number of workers at the plant and y is the annual expenditure at the plant (in dollars). Compute $\frac { \mathrm { d } y } { \mathrm {~d} x }$ at a production level of 23,000 CDs per day and $x = 99$ . Round your answer to two decimal places.

Accepted Answer

The answer of The number P of CDs the Snappy...

Compute the derivative. $\frac { \mathrm { d } } { \mathrm { d } x } \left[ \left( x ^ { 3 } + 2 x \right) \left( x ^ { 2 } - x \right) \right] _ { x = - 2 }$

Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ using implicit differentiation. $\frac { e ^ { x } } { y ^ { 2 } } = 16 + e ^ { y }$

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. $y = \frac { 2 x + 2 } { 4 x - 5 }$

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Probability

Random Variables and Statistics

Introduction to the Derivative

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

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Exam 11: Techniques of Differentiation

Compute the derivative. ddx[(x3+2x)(x2−x)]x=−2\frac { \mathrm { d } } { \mathrm { d } x } \left[ \left( x ^ { 3 } + 2 x \right) \left( x ^ { 2 } - x \right) \right] _ { x = - 2 }dxd​[(x3+2x)(x2−x)]x=−2​

Find dy dx\frac { \mathrm { d } y } { \mathrm {~d} x } dxdy​ using implicit differentiation. exy2=16+ey\frac { e ^ { x } } { y ^ { 2 } } = 16 + e ^ { y }y2ex​=16+ey

Calculate dy dx\frac { \mathrm { d } y } { \mathrm {~d} x } dxdy​ . You need not expand your answer. y=2x+24x−5y = \frac { 2 x + 2 } { 4 x - 5 }y=4x−52x+2​