Question
Differentiate the following w.r.t. x. : \begin{equation}
x^3 \log x
\end{equation}

Answer

Let $y=x^3 \log x$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{\mathrm{d} y}{\mathrm{~d} x} & =\frac{\mathrm{d}}{\mathrm{d} x} x^3 \log x \\
& =x^3 \frac{\mathrm{d}}{\mathrm{d} x}(\log x)+(\log x) \frac{\mathrm{d}}{\mathrm{d} x}\left(x^3\right) \\
& =x^3 \times \frac{1}{x}+(\log x)\left(3 x^2\right) \\
& =x^2+3 x^2 \log x
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free