Question

Find the derivative of $x^2$ with respect to $\log x$.

Answer 1

Let, $y=x^2$ and $z=\log x$. We are to find $\frac{dy}{dz}$.

This gives $\frac{dy}{dx}=2x$ and $\frac{dz}{dx}=\frac{1}{x}$.

Now $\frac{dy}{dz}=\frac{\frac{dy}{dx}}{\frac{dz}{dx}}=2x^2$.