If y=[ ( ( x))]^2, find d y d x - Vidyadip

Question

If $y=[\log (\log (\log x))]^2$, find $\frac{d y}{d x}$

✓

Answer

$
\begin{aligned}
& \quad y=[\log (\log (\log x))]^2 \\
& \therefore \frac{d y}{d x}=\frac{d}{d x} \cdot[\log (\log (\log x))]^2 \\
& =2[\log (\log (\log x))] \cdot \frac{d}{d x}[\log (\log (\log x))] \\
& =2 \log [\log (\log x)] \times \frac{1}{\log (\log x)} \cdot \frac{d}{d x}[\log (\log x)] \\
& =\frac{2 \log [\log (\log x)]}{\log (\log x)} \times \frac{1}{\log x} \cdot \frac{d}{d x}(\log x) \\
& =\frac{2 \log [\log (\log x)]}{\log (\log x)} \times \frac{1}{\log x} \times \frac{1}{x} \\
& =\frac{2 \log [\log (\log x)]}{x \cdot \log x \cdot \log (\log x)} .
\end{aligned}
$

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