Say I have the following:
$$f(t) = \int_0^t{e^{s^3\sin(t)}ds}$$
How do I compute $f'(t)$?
My first thought was to use FTC, but the $s$ variable makes this confusing. I'm not completely sure where partial derivatives would come into play, either, given that $f$ is defined as a single-variable function. I thought LIR was the correct approach, but was told I was wrong.
This is homework for a non-linear optimization problem.
Edit
When I apply LIR, this is what I get:
$$f'(t)=e^{t^3\sin t}+\int_0^ts^3e^{s^3\sin t}\cos tds$$