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

Derivatives & Second-Order Derivatives · Question 82 of 96

Question 82

HardOriginal question

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

- 2 e^{- x} \sin x

Correct answerYour answer

2 e^{- x} \cos x

Correct answerYour answer

e^{- x} \cos x

Correct answerYour answer

2 e^{- x} \sin x

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$\frac{dy}{dx} = -e^{-x}\cos x - e^{-x}\sin x = -e^{-x}(\cos x + \sin x)$ .
$\frac{d^2y}{dx^2} = e^{-x}(\cos x + \sin x) - e^{-x}(\cos x - \sin x) = 2e^{-x}\sin x$ .

Worth noting

$-2e^{-x}\sin x$ slips a sign: the $-$ of $e^{-x}$ meets the $-$ already in front of the first derivative.

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

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