I'm mostly curious as to if the way I've went about solving this is correct, or if there is a more simple way to get the answer.
So I first evaluated the top section
And when I did that I got sin(e^x)
With that, I replaced the upper bound of the integral with sin(e^x) and integrated sin(t^2) dt
My Resulting equation was
Which I then tried to differentiate using the product rule of three parts first being (2sin(e^x)), second sec(sin^2(e^x)), and the third tan(sin^2(e^x)). The resulting derivative I got was
So thats what i've done, any tips or suggestions would be appreciated mostly was hoping to get some feedback about the method I used and if its the best/easiest method for these types of problems.