What is the derivative of $x^{3}$ with respect to $x^{2}$ ?

\frac{2}{3 x}

Correct answerYour answer

\frac{3 x}{2}

Correct answerYour answer

x

Correct answerYour answer

3 x^{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Let $u = x^{3}$ and $v = x^{2}$ ; then $\frac{du}{dv} = \frac{du/dx}{dv/dx}$ , with $x$ as the parameter.
$\frac{3x^{2}}{2x} = \frac{3x}{2}$ .

Worth noting

$3x^{2}$ is the derivative with respect to $x$ ; it still has to be divided by $\frac{d}{dx}(x^{2}) = 2x$ .

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

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

What is the derivative of x3x^{3}x3 with respect to x2x^{2}x2?