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# Derivatives - Product, Chain Rules, Application type

Differentiate the following problems. Assume A, B and C are constant. Show all work.

f(x)=2ex+x2

P=3t3+2et

y=5*2x-5x+4

P(t)=12.41(0.94)t

y=10x+10/x

y=t2 + 5 ln t

y=x2 + 4x - 3 ln x

Solve the following problem and show work

For the cost of function C = 1000 + 300 ln q (in dollars) find the cost and the marginal cost at a production level of 500. Give answer in economic terms.

In the following find the derivative of the functions.

f(x)=(x+1)99

w=(t2+1)100

w=(5r-6)3

f(t)=e3t

y=e-4t

P=50e-0.6t

y=12-3x2+2e3x

f(x)=6e5x+e-x2

w=e-3t(squared)

Solve the following problems and show work.

The cost of producing a quantity, q, of a product is given by C(q)=1000+30e0.05q dollars.
Find the cost and the marginal cost when q=50. Give answers in economic terms.

If f(x)=x2(x3+5), find f ' (x) two ways: by using the product rule and by multiplying out before taking the derivative. Are the results the same? Should they be?

For the following, find the derivative and show work. Assume that a, b, c and k are constants.

f(x)=xex

y=x*2x

y=t2(3t+1)3

y=(t2+3)et

y=(t3-7t2+1)et

f(t)=5/t+6/t2

Solve the following and show work.

If f(x)=(3x+8)(2x-5), find f ' (x) and f "(x)

#### Solution Preview

The solution file is attached.

Differentiate the following problems. Assume A, B and C are constant. Show all work.

f(x)=2ex+x2

f'(x) = 2e^x + 2x

P=3t3+2et

dP/dt = 9t^2 + 2e^t

y=5*2x-5x+4

dy/dx = 5 * a^x * ln(a) - 5

P(t)=12.41(0.94)t

P'(t) = 12.41 * 0.94^t * ln(0.94) = -0.7679 * 0.94^t

y=10x+10/x

dy/dx = (10^x) ln(10) - 10/x^2 = 2.3026 * 10^x - 10/x^2

y=t2 + 5 ln t

dy/dt = 2t + (5/t)

y=x2 + 4x - 3 ln x

dy/dx = 2x + 4 - (3/x)

Solve the following problem and show work

For the cost of function C = 1000 + 300 ln q (in dollars) find the cost and the marginal cost at a production level of 500. Give answer in economic terms.

C(q) = 1000 + 300 ln(q)
(a) C(500) = 1000 + 300 ln(500) = \$2864.38
(b) Marginal cost = C'(q) = ...

#### Solution Summary

The solution file contains solutions to many questions on derivatives (product rule, chain rule etc including application type problems).

\$2.19