I'm trying to use Leibniz's rule for differentiation under the integral sign for the following problem:
$I_n(x)=\int_{a}^{x} (x-t)^{n-1}f(t)dt$
The answer should be $(n-1)f(x)$ but I got a totally different one, may someone guide me through this?
According to wikipedia if we declare $f(x,t)=(x-t)^{n-1}f(t)$ then the differentiation result is:
$f(x,x)+\int_{a}^{x} \frac{\partial}{\partial x}f(x,t) dt=\int_{a}^{x} \frac{\partial}{\partial x}f(x,t) dt=\int_{a}^{x} (n-1)(x-t)^{n-2}f(t) dt$
What is my mistake?