# Double partial differentiation with respect to variables located at the integral limit

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