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.


1 Answer 1


You can use the Leibiz integral rule to calculate the answer. http://en.wikipedia.org/wiki/Leibniz_integral_rule

  • $\begingroup$ I'm not sure I completely understand how to use this... I can't seem to find anything about bounds with multiple variables? $\endgroup$
    – Lucy
    Oct 7, 2013 at 22:00
  • $\begingroup$ Since $t$ and $x$ are independent variables, you can treat $t$ as an unknown constant (unless there is some explicitly specified relationship between them). $\endgroup$
    – svenkatr
    Oct 7, 2013 at 22:26

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