Exam 13: Additional Differentiation Topics

Find y' if y = log .

Find y' if y =

If f(x)= x( + 9x + 3),find the rate of change of f'.

The location of an Earth-orbiting satellite in a grid centered at the center of the Earth is given by Find .

Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and unskilled labor x satisfy 384 = (x + (y + .Find ,the rate of change of skilled labor hours with respect to unskilled labor hours.

Find y' if y = .

Find all of the higher-order derivatives of x(t)= - 3 - x.Use your graphing calculator to graph x(t)and x'(t)on the same axes.Verify that when x(t)is decreasing (sloping downward),the value of x'(t)is negative.Repeat this for x'(t)and x''(t),for x''(t)and x'''(t),and for x'''(t)and (t).

If f(x)= ,find f''(x).

The demand function for a manufacturer's product is given by p = 300 - ,where p is the price per unit when q units are demanded. (a)Determine the point elasticity of demand when q = 5. (b)For q = 5,is demand elastic,inelastic,or does it have unit elasticity? (c)For what value of q does demand have unit elasticity?

Use your graphing calculator to graph the equation y = ln( )- 2 + + 11.Zoom in on the graph to approximate the roots of the equation.Use Newton's method to verify your results.

Find y' if y = .

Differentiate: f(x)=

Determine the point elasticity η of the demand equation pq = 81,where p > 0 and q > 0.

Find y' if y = .

Find y' if y = ln(4x + 5).

Find y' if y = (4x + 5).

If f(x)= ,find f''(x).

Find y' if y =

If f(x)= ,then f'(x)=

The position of an object moving on the x-axis is given by x(t)= 12 + 32t +3,where t is the time in seconds.Find x''(t),the acceleration of the rock,when t = 6.