Differentiation — Maths STD 12 Science — Question

Differentiating w.r.t. x, we get

$\begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}[\log \{\log (\log x)\}]^2 \\ & =2 \cdot \log \{\log (\log x)\} \times \frac{d}{d x}[\log \{\log (\log x)\}]\end{aligned}$

$\begin{aligned} & =2 \cdot \log \{\log (\log x)\} \times \frac{1}{\log (\log x)} \cdot \frac{d}{d x}[\log (\log x)] \\ & =2 \cdot \log \{\log (\log x)\} \times \frac{1}{\log (\log x)} \times \frac{1}{\log x} \times \frac{d}{d x}(\log x) \\ & =2 \cdot \log \{\log (\log x)\} \times \frac{1}{\log (\log x)} \times \frac{1}{\log x} \times \frac{1}{x} \\ & =2 \cdot\left[\frac{\log \{\log (\log x)\}}{x \cdot \log x \cdot \log (\log x)}\right] .\end{aligned}$