Differentiate w.r.t. x, the function, log7 (log x) - Vidyadip

Question

Differentiate w.r.t. x, the function, log₇ (log x)

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Answer

Let y = log₇ (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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