If we have $f\left(x\right)$ $x$ real and $f$ a real function. The rigorous definition of the derivative of the function is 
$$
\lim\_{h\rightarrow 0} \frac{f\left(x+h\right)-f\left(x\right)}{h}
$$
**My question is**
If we have $f(x,p(x))$, where $f$ and $p$ real functions, $f$ is an unknown function. What is the rigorous derivative of $f$ with respect $x$?