# derivative of multiple integral

#### devilishruby

I have a problem in derivative of multiple integrals. for example i don't know how can I do it for the below question. would you please help me to solve it? thanks
$$\displaystyle A= \int \int q(y,z)(Ln|z|+tr(z^{-1}(x'x-2 x' y+y' y)))dy dz$$
where x,y,z are vectors

we want derivative of A wrt q(y,z).

#### chiro

MHF Helper
Hey devilishruby.

You should first find out what is not independent to q and write that as a function of q.

After that you should note that if you differentiate anything in a partial derivative manner and that variable is independent to everything else then you just treat it as a constant.

Also it would help you if you expressed your integral in terms of anti-derivatives and used the fundamental theorem of calculus.

https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

You will have to do to it twice since you have a double integral.