What is the derivative of (sin x)/x?

Derivatives & Second-Order Derivatives · Question 16 of 96

Question 16

MediumOriginal question

What is the derivative of $\frac{\sin x}{x}$ ?

\frac{- x \cos x + \sin x}{x^{2}}

Correct answerYour answer

\frac{x \cos x - \sin x}{x^{2}}

Correct answerYour answer

\cos x

Correct answerYour answer

\frac{x \cos x + \sin x}{x^{2}}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Quotient rule: $\left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2}$ , with $u = \sin x$ and $v = x$ .
This simplifies to $\frac{x \cos x - \sin x}{x^{2}}$ .

Worth noting

$\frac{- x \cos x + \sin x}{x^{2}}$ has the numerator the wrong way round: it is $u'v - uv'$ , not $uv' - u'v$ .

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

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