Question

LEGEN...waitforit...DARIDDLE:

Simple Calculus Question:

when is this true:

\[\frac{\rm d}{\rm dx} \left(\begin{matrix} \int f(x) \rm dx\end{matrix}\right) \ne \int \left(\begin{matrix} \frac{\rm d}{\rm dx} \rm f(x)\end{matrix}\right)\rm dx \]

Answer 1

its always true, unless we define some initial values (for constant of integration)
example
when f(x) has a constant in it.
say,
f(x) = x+3

left side = x+3
right side is just x+c
if c' = 3, then its becomes false

when f(x) does not have a constant in it.
say,
f(x) = x^2+x

left side = x^2+x
right side is just x^2+x+c
if c=0, then its becomes false

Answer 2

close enough.

Answer 3

the answer was actually when f(x) = k where k is a constant...but i suppose it applies to your examples as well