   Chapter 2.5, Problem 12E

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# Find the derivative of the function. f ( x ) = 1 x 2 − 1 3

To determine

To find:

Derivative of the function

Solution: f'x=-2x3(x2-1)x2-11/3

Explanation

1) Rule:

a) Power rule combined with chain rule: If n is any real number and u = g(x) is differentiable then dgxndx=ngxn-1*g'(x)

b) Difference rule: d(fx-g(x))dx=d(f(x))dx-d(g(x))dx

c) Constant function rule: d(C)dx=0

d)  Power function rule: d(xn)dx=nxn-1

2) Given: fx=1x2-13

3) Calculation:

First rewrite equation as

fx=x2-1-1/3

f'x=dx2-1-1/3dx

By the power rule combined with chain rule,

f'x=-13x2-1-43*d

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