Find derivatives of d d x (x x) - Vidyadip

Question

Find derivatives of $\frac{d}{d x}(x \times \ln x)$

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Answer

Using,
$\frac{d}{d x}\left[f_1(x) \times f_2(x)\right]=f_1(x) \frac{d f_2(x)}{d x}+f_2(x) \frac{d f_1(x)}{d x}$
Here, $f_1(x)=x$ and $f_2(x)=\ln x$
$
\begin{aligned}
\therefore \quad \frac{ d }{ dx }( x \times \ln x ) & = x \times \frac{ d (\ln x )}{ dx }+\ln x \times \frac{ dx }{ dx } \\
& = x \times \frac{1}{ x }+\ln x \times 1= 1 +\ln x
\end{aligned}
$

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