time derivative of a function with one variable depending on time

Question

With $f(x)$ a function of $x$ and $x(t)$ a function of time does $\frac{df(x)}{dt}=0 $ ?

thanks.

Answer 1

No it is not $0$.

By the chain rule;

$\frac{d(f(x(t)))}{dt} = f'(x(t))\cdot x'(t)$