Exam 13: Additional Differentiation Topics

Find y' if y = ln .

The altitude (in feet)of a rocket t seconds into flight is given by h = - + 80 + 750t + ln t + 200,t ≥ 0.Use Newton's method to approximate when the rocket will hit the ground.

Find y' if y = .

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

Medical research has found that between heartbeats the pressure in the aorta of a normal adult is a function of time and can be modeled by the equation P = 95 .Find ,the rate at which the pressure changes with respect to time.

The total cost for a product is given by C(x)= 1750 + 300 ln(x + 2).Find the rate of change of C''(x).

The total revenue from the sales of a certain product are given by R(x)= .Find the marginal revenue.

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

The total cost for a product is given by C(x)= 36 + 5 ln(3x + 9).Find the rate of change of C''(x).

If the total profit (in dollars)from the sale of x radios is P(x)= 50x - 0.05 - 700 + 5 ln(x),use Newton's method to approximate the break-even points for profit.(Note: There are 2 break-even points; one is between 10 and 50,and the other is between 900 and 1000.)

The Reynolds number is a quantity that relates to the flow of a liquid.If it is given by the equation where x is the radius of the tube the liquid flows through and A and B are positive constants,find .

If the position of a particle moving along the x-axis at a given time is given by x(t)= + 3 - 5t + 12,find all the higher-order derivatives of this function.

Find y' if y = .

If y = × ,then find y'.

The percentage p of a certain radioactive element present after t years is given by p = .Find .

If y = ,use logarithmic differentiation to find y'.

If the cost to produce x units of a product is C(x)= 0.5 + 9x + 440 and the marginal cost function is C'(x),then find C''(x),the rate of change of the marginal function with respect to x.

If y = ,then find y'.

If y = x ln x,then find .

Differentiate: h(x)=