Question

Derivative of the function $f\left(x\right)={\log }_5\left({\log }_{7}x\right),x>7$ is ?

• A. $\frac{1}{x\left(\ln 5\right)\left(\ln 7\right)\left({\log }_{x}7\right)}$
• B. $\frac{1}{x\left(\ln 5\right)\left(\ln x\right)}$
• C. $\frac{1}{x\left(\ln x\right)}$
• D. None of these

Answer 1

The correct option is B $\frac{1}{x\left(\ln 5\right)\left(\ln x\right)}$

$\frac{dy}{dx}=\frac{1}{log5}\times \frac{1}{lo{g}_{7}x}\times \frac{d}{dx}lo{g}_{7}x$

$\frac{dy}{dx}=\frac{1}{log5}\times \frac{1}{lo{g}_{7}x}\times \frac{1}{log7}\times \frac{1}{x}$

$\frac{dy}{dx}=\frac{1}{x\times ln5\times lnx}$