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Chapter 2: Q. 21 (page 210)

Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

f(x)=1x3+1

Short Answer

Expert verified

The derivative of f(x)is:

localid="1648393361184" f'(x)=-3x2x3+12

Step by step solution

01

Step 1. Given information:

The function is:

f(x)=1x3+1

02

Step 2. Differentiate the function with respect to x using quotient rule:

f'(x)=ddx1x3+1=x3+1ddx1-1.ddxx3+1x3+12=x3+1.0-3x2+0x3+12=0-3x2x3+12=-3x2x3+12

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