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Derivatives & Second-Order Derivatives · Question 6 of 96

Question 6

MediumOriginal question

Differentiate log⁡(sin⁡x)\log(\sin x) with respect to xx.

Options for question 6

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. By the chain rule, ddxlog⁡u=1ududx\frac{d}{dx}\log u = \frac{1}{u}\frac{du}{dx} with u=sin⁡xu = \sin x.

  2. 1sin⁡x⋅cos⁡x=cot⁡x\frac{1}{\sin x} \cdot \cos x = \cot x.

Worth noting

1sin⁡x\frac{1}{\sin x} stops at the logarithm and forgets to multiply by the derivative of sin⁡x\sin x.

Concept
The chain rule with a logarithm
Typical time
90 s
Your time
—
The rule this testsThe rules of differentiation
Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.

Practise this chapter →

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.