Question

Differentiate log x with respect to x.     ​

Answer 1

$\bold \pink{Answer}$

$\sf \: y \: = ({log \: x})^{x}$

$\sf \: Taking \: log \: on \: both \: sides \: , \: we \:get$

$\sf \: log \: y \: = \: x \: log \: ( \: log \: x)$

$\sf \: Differentiating \: w.r.t.x , \: we \: get,$

$\sf \: \frac{1 \: dy}{ \: y \: dx} = \frac{x}{log \: x} \: \times \frac{1}{x} \: + \: log \: (log \: x)$

$\sf \: \frac{dy}{dx} \: = ({logx})^{x} ( \frac{1}{logx} + log(logx))$