# Derivative vs integral

1. Feb 7, 2006

### matness

it is simple but i have some suspession about it
when the integral and derivative of some func can commute ?
for ex. is it possible to say
$$\frac{{\partial ^{} }}{{\partial y^{} }}\int_a^b {f(x,y)dx} = \int_a^b {\frac{{\partial ^{} }}{{\partial y^{} }}f(x,y)dx}$$

or are there any condition for f(x,y) to satisfy?(?any toplogical condition other than f integrable)

Last edited: Feb 7, 2006
2. Feb 7, 2006

### quasar987

I my book, the theorem reads: "If M(x,y) and dM/dy are continuous functions on some region R, then < what you wrote >"

I assume it is implied that the region R contains the interval [a,b]

3. Feb 8, 2006