Differentiate: $\displaystyle f(x) = \int_{0}^{x} \frac {x}{1 + t^2 + sin^2t}dt$

I am not sure how to do this, since there are 2 different variables in the integral (x and t).

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- Aug 3rd 2010, 05:31 AMSyNtHeSiSDerivative of an integral
Differentiate: $\displaystyle f(x) = \int_{0}^{x} \frac {x}{1 + t^2 + sin^2t}dt$

I am not sure how to do this, since there are 2 different variables in the integral (x and t). - Aug 3rd 2010, 05:34 AMAckbeet
Take the x out of the integral (assuming it doesn't depend on t, which it doesn't look like it). Then use the product rule on x and the integral.