If y = e^x sin x, what is d^2y/dx^2?

Question 73

MediumOriginal question

If $y = e^{x} \sin x$ , what is $\frac{d^2y}{dx^2}$ ?

2 e^{x} \cos x

Correct answerYour answer

\sqrt{2} e^{x} \sin{\left(x + \frac{\pi}{4} \right)}

Correct answerYour answer

- 2 e^{x} \cos x

Correct answerYour answer

2 e^{2 x} \sin^{2}{\left(x + \frac{\pi}{4} \right)}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

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

Worth noting

$\sqrt{2} e^{x} \sin{\left(x + \frac{\pi}{4} \right)}$ stops at the first derivative; $\frac{d^2y}{dx^2}$ differentiates it once more.

Ten questions from Derivatives & Second-Order Derivatives, at your own pace.