Math 1325 calculus for business and social sciences find

Question

MATH 1325 CALCULUS FOR BUSINESS AND SOCIAL SCIENCES

1. Find the derivative of each function. Be sure to simplify your answer.

a) y = (2x³ + 9x)⁵

b) y = 8√(4x² + 7)

c) y = 0.2e^5x

d) y = 3·4^{x^2+2}

e) y = log₅(3x² - 7x)

f) y = ln(2x + 5)

2. Find the derivative of each function. Be sure to simplify your answer.

a) y = x²+4x/(3x³+2)⁴

b) y = x²e^-2x

c) y = (3x+1)ln(x-1)

d) y = x³-1/ln x

e) y = e^x/2x+1

f) y = log₃(x²+2x)⁴

3. Suppose that the total revenue from the sale of x televisions is given by R(x) = 1000(1 - x/500)².

a) Find the marginal revenue function, R'(x).

b) Find and interpret R'(400), R'(500), and R'(600).