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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.

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