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Chain Rule, Log Differentiation & Rate of Change · Question 11 of 130

Question 11

MediumOriginal question

Read the two statements and choose the correct option.

I. ddxsin⁡2x=sin⁡2x\frac{d}{dx}\sin^{2} x = \sin 2x.

II. ddxsin⁡(x2)=cos⁡(x2)\frac{d}{dx}\sin(x^{2}) = \cos(x^{2}).

Options for question 11

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. I: 2sin⁡xcos⁡x=sin⁡2x2\sin x\cos x = \sin 2x. True.

  2. II: the inner x2x^{2} gives a factor 2x2x, so it is 2xcos⁡(x2)2x\cos(x^{2}). False.

Worth noting

sin⁡2x\sin^{2} x squares the sine; sin⁡(x2)\sin(x^{2}) squares the angle, and the two differentiate differently.

Concept
\(\sin^{2} x\) and \(\sin(x^{2})\)
Typical time
90 s
Your time
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