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Derivatives & Second-Order Derivatives · Question 58 of 96

Question 58

MediumOriginal question

What is the derivative of sin⁡x\sin x with respect to cos⁡x\cos x?

Options for question 58

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. d(sin⁡x)d(cos⁡x)=cos⁡x−sin⁡x\frac{d(\sin x)}{d(\cos x)} = \frac{\cos x}{-\sin x}.

  2. =−cot⁡x= -\cot x.

Worth noting

cot⁡x\cot x forgets that the derivative of cos⁡x\cos x is −sin⁡x-\sin x.

Concept
Derivative of one function with respect to another
Typical time
90 s
Your time
—
The rule this testsParametric functions
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.