# Derivative $dy/dx$ of a complex $f(x)\log{f(x)}$ function with respect to $x$?

I am trying to take the derivative of the function. The fundamental way seems tedious for me. I apologize for that. I was trying to find a closed-form expression of the derivative $$dy/dx$$ for such a function.

Note that: $$y$$ is continuous and weakly differentiable/ differentiable for all value of $$x\ge0$$.

$$y = \left\{ {\sum\limits_{i = 1}^M {{f_{1i}}\left( x \right){f_{2i}}\left( x \right)} } \right\}\log \left\{ {\sum\limits_{i = 1}^M {{f_{1i}}\left( x \right){f_{2i}}\left( x \right)} } \right\}$$

Is there any theorem that will make it easy to take the derivative in closed-form? Is it possible to take the closed-form of the above expression? Thank you.