If y = cos(x^2 ), what is d^2y/dx^2?

- 4 x^2 cos(x^2 ) - 2 sin(x^2 )

Question 77

HardOriginal question

If $y = \cos{\left(x^{2} \right)}$ , what is $\frac{d^2y}{dx^2}$ ?

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

Correct answerYour answer

4 x^{2} \cos{\left(x^{2} \right)} + 2 \sin{\left(x^{2} \right)}

Correct answerYour answer

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

Correct answerYour answer

4 x^{2} \sin^{2}{\left(x^{2} \right)}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

First derivative: $\frac{dy}{dx} = - 2 x \sin{\left(x^{2} \right)}$ .
Differentiate again: $\frac{d^2y}{dx^2} = - 4 x^{2} \cos{\left(x^{2} \right)} - 2 \sin{\left(x^{2} \right)}$ .

Worth noting

$- 2 x \sin{\left(x^{2} \right)}$ stops at the first derivative; $\frac{d^2y}{dx^2}$ differentiates it once more.

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