Leibniz rule or not? improper integral?

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If $f(x)=(\int_0^x e^{-t^2}dt)^2$ and $g(x)$=$\int_0^1{e^{-x^2(1+t^2)}\over(1+t^2)}dt$ then $f'(\sqrt\pi) + g'(\sqrt\pi)$ is equal to?? i tried to use Leibniz rule and differentiate with respect to x but got got stuck in between could someone help me