# 14 Derivative Problems : Product Rule, Quotient Rule, Chain Rule, First and Second Derivative and Finding Maximum or Minimum

Rules and Applications of the Derivative

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1. Use the Product Rule to find the derivatives of the following functions:

a. f(X) = (1- X^2)*(1+100X)

b. f(X) = (5X + X^-1)*(3X + X^2)

c. f(X) = (X^.5)*(1-X)

d. f(X) = (X^3 + X^4)*(30 + X^2)

2. Use the Chain Rule to find the derivatives of the following functions:

a. f(X) = (1- X^2)^5

b. f(X) = (5X + X^-1)^-1

c. f(X) =(1-X)^2

d. f(X) = (X^3 + X^4)^3

3. Use the Quotient Rule to find the derivatives of the following functions:

a. f(X) = 100/X^4

b. f(X) = 1/(5X + X^2)

c. f(X) =5/(1-X)

4. For each of the following functions find the 1) first and second derivative, 2) explain whether or not the function has a maximum or a minimum, and how you reached that conclusion, and 3) the value of the maximum or minimum

a. f(X) = 5X^2 - 2X

b. f(X) = 1000X - X^2

c. f(X) = 8X^3 - 4X^2

sorry about that forgot the powers

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#### Solution Summary

Fourteen derivative problems are solved regarding Product Rule, Quotient Rule, Chain Rule, First and Second Derivative and Finding Maximum or Minimum. The solution is detailed and well presented.