Question

If $y={\log }_7(\log x)$, then $\frac{dy}{dx}$ is equal to

• A. $\frac{1}{x\log x\log 7}$
• B. $\frac{-1}{x\log x\log 7}$
• C. $\frac{1}{x\log x}$
• D. None of these

Answer 1

Answer: (A)

A. 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, $\frac{dy}{dx}=\frac{1}{\log 7}\frac{d}{dx}(\log (\log x))$
$=\frac{1}{\log 7}\frac{1}{\log x}\cdot \frac{d}{dx}(\log x)=\frac{1}{x\log 7\log x}$