Order of differentiation and integration

[toptrial]

I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to?
$$\frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt$$

 

[tiny-tim]

I guess the following identity isn't right. Can anyone tell me what the LHS is really equal to?
$$\frac{\partial}{\partial x}\int_{-\infty}^\infty\int_0^x f(s,t) dsdt = \int_{-\infty}^\infty f(x,t)dt$$

Hi toptrial!

Looks ok to me (unless there's a convergence difficulty).

Do you have a particular f(s,t) in mind?