Differentiate w.r.t. x, the function, log_7 ( x) - Vidyadip

Question

Differentiate $w.r.t. x,$ the function, $log_7\ (\log x)$

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Answer

Let $y = log_7 (\log x) = \frac{\log (\log x)}{\log 7} ...($by change of base formula$)$
The function is defined for all real numbers $x > 1. $
Therefore $\frac{d y}{d x}=\frac{1}{\log 7} \frac{d}{d x} (\log (\log x))$
$\frac{d y}{d x} = \frac{1}{\log 7} \frac{1}{\log x} \cdot \frac{d}{d x}(\log x)$
$\frac{d y}{d x} = \frac{1}{x \log 7 \log x}$

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