What is d/dx(cos(3 x^2 ))?

Question 13

MediumOriginal question

What is $\frac{d}{dx}\left(\cos{\left(3 x^{2} \right)}\right)$ ?

- \sin{\left(3 x^{2} \right)}

Correct answerYour answer

6 x \sin{\left(3 x^{2} \right)}

Correct answerYour answer

- 12 x \sin{\left(3 x^{2} \right)}

Correct answerYour answer

- 6 x \sin{\left(3 x^{2} \right)}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Use the chain rule: differentiate the outer function, then multiply by the derivative of what is inside it.
$\frac{d}{dx}\left(\cos{\left(3 x^{2} \right)}\right) = - 6 x \sin{\left(3 x^{2} \right)}$ .

Worth noting

$- \sin{\left(3 x^{2} \right)}$ differentiates the outside only and drops the inside's derivative.

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