# derivative of an integral which has a bound with multiple variables?

I want to find the derivative with respect to x of:

$$\int_0^{{\frac{x}{\sqrt4t}}} {e}^{-s^2}\,\mathrm{d}s$$

where t and x are both independent variables. I thought you should use the fundamental theorem of calculus. However, since the upper bound of the integral is in terms of t and x, does this complicate the question? Do I need to somehow use the chain rule to get it in terms of just x? Any help would be greatly appreciated.

• Since $t$ and $x$ are independent variables, you can treat $t$ as an unknown constant (unless there is some explicitly specified relationship between them). Oct 7, 2013 at 22:26