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I have an integration over variable $x$, the limits of the integration are variables ($z,y$). I would like to make double partial differentiation for integral equation with respect to $z$ and $y$. Is there any direct method to make the differentiation without starting by performing the integration then make the double differentiation for the output of the integration? The equation is $$\frac{\partial^2}{\partial y \partial z}\int \limits_{az}^{by}\pi\lambda_2 x\left[y^2 - K x^2\right] \exp\left[-N x^2\right] dx$$ where $K, M, N$, and $\lambda_2$ are constant

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