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Chapter 2: Q. 7 (page 232)

The derivatives of the function f(x)=cos3x2that follow are incorrect. What misconception occurs in each case?

(a) Incorrect:f'(x)=(-sinx)3x2+(cosx)(6x).(b) In褋芯r褌械褋t:f'(x)=-sin(6x).

Short Answer

Expert verified

The answer is

Part (a) cos3x2where 3x2is a parameter, so product rule will not be applied.

Part (b) The chain rule will be applied outside the parameter and not inside.

Step by step solution

01

Part (a) Step 1. Given information.

The given function isf(x)=cos3x2.

02

Part (a) Step 2. Explanation.

The function f(x)=cos3x2has a parameter as 3x2. So, product rule will not be applied.

In the given derivative,(-sinx)3x2+(cosx)(6x), product rule is applied.

03

Part (b) Step 1. Explanation.

In the given derivative, -sin(6x), chain rule is applied incorrectly.

It should have been applied outside the sin function.

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Most popular questions from this chapter

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

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