The differential coefficient of $f[\log (x)]$ with respect to $x$ when $f(x) = \log x$ is:

The derivative of $\log |x|$ is

Consider the following statements:
Statement $1$: If $y = \log_{10} x + \log_{e} x$,then $\frac{dy}{dx} = \frac{\log_{10} e}{x} + \frac{1}{x}$.
Statement $2$: $\frac{d}{dx}(\log_{10} x) = \frac{\log x}{\log 10}$ and $\frac{d}{dx}(\log_{e} x) = \frac{\log x}{\log e}$.

The derivative of the function $f(x) = \log_5(\log_7 x)$ for $x > 7$ is:

If $y = \sqrt{\frac{1 + e^x}{1 - e^x}}$,then $\frac{dy}{dx} = $

Find the derivative: $\frac{d}{dx}[(\log_e x)(\log_a x)]$