I am trying to find

$\displaystyle \frac{d}{dx} _{\cos{x}}\int^{3} e^{t^{2}}dt$

I flipped it to:

$\displaystyle \frac{d}{dx} - _{3}\int^{\cos{x}} e^{t^{2}}dt$

So I believe what I have to do is take the derivative of

$\displaystyle e^{cos^{2}{x}}$

Using the chain rule, I get

$\displaystyle e^{cos^{2}{x}} \times -2sin{x}cos{x}$

Since I flipped the integral, I multiply by negative one and get

$\displaystyle 2sin{x}cos{x}e^{cos^{2}{x}}$

But this is not the answer. Can anyone see where I went wrong? Thanks for your time