What is d/dx(sin^3 xcos 3x)?

Chain Rule, Log Differentiation & Rate of Change · Question 27 of 130

Question 27

HardOriginal question

What is $\frac{d}{dx}\left(\sin^{3} x\cos 3x\right)$ ?

3\sin^{2} x\cos 2x

Correct answerYour answer

3\sin^{2} x\cos x\cos 3x

Correct answerYour answer

-9\sin^{2} x\cos x\sin 3x

Correct answerYour answer

3\sin^{2} x\cos 4x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Product rule: $3\sin^{2} x\cos x \cdot \cos 3x + \sin^{3} x \cdot (-3\sin 3x)$ .
$3\sin^{2} x(\cos x\cos 3x - \sin x\sin 3x) = 3\sin^{2} x\cos 4x$ .

Worth noting

$3\sin^{2} x\cos 2x$ takes the derivative of $\cos 3x$ as $+3\sin 3x$ , turning $\cos(x + 3x)$ into $\cos(3x - x)$ .

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.

Ten questions from Chain Rule, Log Differentiation & Rate of Change, at your own pace.