Question

Find the derivative of $y={\log }^3\left(x^2\right)$

Answer 1

$y={\log }^3\left(x^2\right)$

for differentiation we apply chain Rule here

$\frac{dy}{dx}=3{\log }^2\left(x^2\right)\times \frac{1}{x^2}\cdot 2x\times \frac{1}{{\log }_{e}10}$

$\Rightarrow \frac{6}{x}{\log }^2{x}^2\times \frac{1}{{\log }_{e}10}$

$=\frac{6}{x}{\log }^2{x}^2\times \frac{1}{ln10}$