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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

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.

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