Exam 13: Additional Differentiation Topics

Suppose a population is growing according to the equation P = .Find the rate of growth of the population, .

If f(x)= ln ,find .

Suppose you deposit $3000 in a savings account with 4.8% interest compounded monthly.Then A,the amount of money in the account after t years,is given by A = 3000(1.00 .Use logarithmic differentiation to find .

The price $p and demand x for a product are related by 3 + 2xp + 25 = 300,000.Find ,the rate of change of price with respect to demand.

If + = 5,find y'' when x = 1 and y = 2.

If C(x),the cost to produce x units of a product is C(x)= 6 + 11x + 124 and the marginal cost function is C'(x),then find the rate of change of the marginal function with respect to x.

The intensity of an earthquake is measured on the Richter scale.The reading R is given by R = log ,where I is the intensity and is a standard minimum intensity.If = 5,find ,the rate of change of the Richter scale reading with respect to the intensity.

The loudness of sound (L,measured in decibels)perceived by the human ear depends upon intensity levels (I)according to L = 10 log ,where is the standard threshold of audibility.If = 1,find ,the rate of change of the loudness with respect to the standard threshold of audibility.

An object moving along the circle + = 36.What is ,the rate of change of the y-coordinate of the particle with respect to the x-coordinate of the particle?

If y = ,then find y'.

The altitude (in feet)of a rocket t seconds into flight is given by h = - + 20 + 900t + 10,t ≥ 0.Use Newton's method to approximate when the rocket will hit the ground.

If y = ,then find y'.

Suppose a population is growing according to the equation P = .Find the rate of growth of the population, .

Find y' if y = ln( - 3).

If y = ln ,then =

Find if = 6x

Find the second derivative y'' from y = (11 - 3x - 5 ) .

The demand equation for a product is p = 400 - 0.2 .Find the rate of change of quantity with respect to price.

Find an equation of the tangent line to the curve y = ln(x + 3)when x = -2.

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