Question

If $y=\left[\log \right(\log \left(\log x\right)){]}^2,$ then Find $\frac{dy}{dx}$

Answer 1

$y=\left[\log \right(\log \left(\log x\right)){]}^2,$
$\frac{dy}{dx}=2log\left(log\right(logx\left)\right)\frac{d}{dx}log\left(log\right(logx\left)\right).$
$⟹2log\left(log\right(logx\left)\right).\frac{1}{log\left(logx\right)}\frac{d}{dx}log\left(logx\right).$
$⟹2log\left(log\right(logx\left)\right)\frac{1}{log\left(logx\right)}.\frac{1}{logx}.\frac{1}{x}$