I have the following expression (everything is $\in \mathbb R$):
$f(a,b,c)=c\cdot\int_a^b g(t) \cdot h(t,c) \,dt,\quad0\leq a
I now want to differentiate this function with respect to c: $\frac{\delta f(\cdot)}{\delta c} $
I know how $h(\cdot)$ looks, but I have no definition of $g(t)$. Is there any way to get to the desired derivative without knowing $g(t)$?
If it is important, here is the definition of $h(\cdot)$:
$h(t,c)=e^{-t\cdot d\cdot(1-c)},\quad0
Edit: My original question has been answered super, now I wonder If there is also a solution if I whish to differentiate with respect to $a$ or $b$: $\frac{\delta f(\cdot)}{\delta a}$ As I understand it, the Leibniz rule can no longer be applied here, right?