I have one function that is defined:
$$E_x(f)=\int K_\sigma(y-x) \cdot e^{-a\cdot f(y)} \, dy$$
where $y$ is neighboor points of $x$; $f(y)$ is a function of $y$; and $a$ is constant.
I want to take want to calculate derivative of this function with respect to $a$. Could you help me implement it? Thank you
$$ \frac{\partial}{\partial a}E_x(f)=-\int f(y) K_\sigma(y-x)\cdot e^{-a\cdot f(y)}dy $$
see differentiation under the integral sign