How to find derivative of an integral of this type $$f(x) = \int _x^{e^x}\:\left(\sin t^2\right)\,dt$$
How to find the derivative $f'(x)$
Attempt: $\sin (e^{x^2})  e^x$

Here's how to do this.
Substitute the values for the upper and lower limits of the integral into the equation. then multiply by the derivative of that value:
So:
$$f'(x) = e^{x}\sin(e^{2x}) - \sin(x^2)$$
