I have the following integral
$$\int_a^b f(w, t)dt$$
where $w \in \Bbb R^n$ and I need to compute partial derivatives with respect to all components of $w$. How can I apply Leibniz rule to this problem?
Suggested answer:
$$\int_a^b \frac {\partial f(w, t)} {\partial w_i}dt$$ for all $i=1,\ldots,n$.
Best Answer
The answer is to use partial derivative under the integral for all needed component of w: $\int_a^b \frac {\partial f(w, t)} {\partial w_i}dt$ . And we don't need Leibniz rule, since the interval is constant