- #1
AntiStrange
- 20
- 1
How do I know when it is ok to change a derivative into a partial derivative? For example there is something like:
(d/dt)∫f(x,t)dx
then they simplify it to:
∫[∂f(x,t)/∂t]dx
I mean, it sort of makes sense to me, because the integral will be a function of t only so the (d/dt) is fine, but when you bring it inside the integral f(x,t) is a function of both t and x, so a partial is needed... but why is it ok to do this?
(d/dt)∫f(x,t)dx
then they simplify it to:
∫[∂f(x,t)/∂t]dx
I mean, it sort of makes sense to me, because the integral will be a function of t only so the (d/dt) is fine, but when you bring it inside the integral f(x,t) is a function of both t and x, so a partial is needed... but why is it ok to do this?