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Find the derivatives of the functions in Exercises 21–46. 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 is6x52(x2-1)2-(x2-1)332x12x3

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 to x, we get,

f'(x)=ddxx2-13x32-x2-13ddxx32x322=3x2-13-1ddx(x2-1)x32-x2-1332x32-1x3=3x2-12(2x)x32-x2-1332x12x3=6x52x2-12-x2-1332x12x3

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Most popular questions from this chapter

Stuart left his house at noon and walked north on Pine Street for 20minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was 10minutes early for his 12:40appointment. Stuart waited at the office for 10minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.

Differentiate f(x)=3x+x2in three ways. When you have completed all three parts, show that your three answers are the same:

(a) with the chain rule

(b) with the product rule but not the chain rule

(c) without the chain or product rules.

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