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Chapter 2: Q. 33 (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)=x-12(x2-1)3

Short Answer

Expert verified

The required answer is-x2-132x3+6xx2-12x

Step by step solution

01

Step 1. Given Information  

The given function is f(x)=x-12(x2-1)3

02

Step 2. Calculation     

Differentiate both the sides with respect tox, we get,

f'(x)=ddxx-12x2-13+x-12ddxx2-13=-12x-12-1x2-13+x-123x2-13-1ddxx2-1=-12x-32x2-13+x-123x2-12(2x)=-x2-132x3+6xx2-12x

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