Exam 13: Additional Differentiation Topics

Find y' if y = ln .

Find y' if y =

Find y' if y = .

If the position of a particle moving along the x-axis at a given time is given by x(t)= + 5 - 7t + 19,find all the higher-order derivatives of this function.

Find y' if y = ln( )+ x.

If y = ( + 3x + ,then y'' =

An approximation of one root of - 8x + 4 = 0 is = 1.Apply Newton's method twice to find the approximation .

The volume of a company's sales y (in thousands of dollars)is related to its advertising expenditures x (in thousands of dollars)by the equation Find .

Find y' if y = .

If y = ln ,then find .

If p = ,find the rate of change of p with respect to q when q = 2.

Use implicit differentiation to find y'' from 3 - xy + 5 = 0.

If + 3 = 8,use implicit differentiation to find and simplify your answer.Note: should not appear in your final answer.

Differentiate: f(x)=

The height h(t)of a rock thrown upward from the ground at a speed of 132 feet/sec is given by h(t)= 132t - 16 ,where t is the time measured in seconds.Find ,the acceleration of the rock at time t.

Determine the point elasticity η of the demand equation p = - + 30,where p > 0 and q > 0.

The total cost for a product is given by C(x)= 212 + 3 ln(2x + 1).Find the rate of change of C''(x).

Differentiate: f(x)= (10x - 4)∙

The volume of a company's sales y (in thousands of dollars)is related to its advertising expenditures x (in thousands of dollars)by the equation xy - 11x + 25y = 0.Find .

If + = 4,use implicit differentiation to find and simplify your answer.Note: should not appear in your final answer.