The question I have is two integrals mutliplied with different bounds
$$\alpha_0(x)=\int_x^1\exp\left(\frac{-\varphi\lambda^2}2\right)d\lambda\cdot\left(\int_0^1\exp\left(\frac{-\varphi\lambda^2}2\right)d\lambda\right)$$
What I would like to do is differentiate this with respect to $x$, but am not sure how to do so considering that I have the two integrals multiplied by eachother.
What is f '(alpha0(x))
I understand that the problem would be simple if they were added/subtracted.
I understand from the Fundamental Law of Calculus that the $x$ will replace the $\lambda$ when I differentiate a single integral, just not sure how to approach with the double integral.
I know that an analytical solution is definitely possible.
Thank you.