calculus

Does anyone know if the domain of a derivative is the same as the domain of the original function ?

y = |x| is defined for all x, but y' is not defined at x = 0.

Therefore no.

it's a subset

everywhere where the function is continuous

>>3
incorrect. Differentiable implies continuity, not the other way round.

>>3
maybe he meant anywhere the function is differentiable

yeah, you're right.
i was thinking continuous as in a smooth line
(yes, i realize that's also wrong)

this got me thinking though
given y=x with the domain [a,b]
is dy/dx's domain (a,b)?
and what if (a,b) were the domain for y=x?

>>6
There are two ways I've seen this handled:
1) Only define differentiability on the interior of the function's domain.
2) Define differentiability everywhere on the function's domain.

#2 presents the somewhat non-intuitive notion that a function which is differentiable on a set S may not be differentiable on all points of S in a superset of S. For instance, y = |x| is differentiable on [0,1] (including at 0), but not on [-1,1].
#1 avoids this problem - any function which is differentiable on the interior of a set S is differentiable on all points of the interior of S in a superset of S. However, you are no longer able to talk about the differentiability of the function on the boundary of the domain.

In fact, differentiable functions are only a very small portion of continuous functions.  Must continuous functions are non-differentiable.

http://en.wikipedia.org/wiki/Weierstrass_function#Density_of_nowhere-differentiable_functions

Read "density of nowhere differentiable functions."

>>8
lol wiener measures

calculus is fucking awesome

fuck yeah!!

I wants lots and lots of some delectable pot!

Marijuana MUST be legalized.