Question

how to find the derivative of absolute value? Can someone give a demo? (explanations appreciated)

Answer 1

dosent the function have to be simply connected?

Answer 2

isnt that the integral?

Answer 3

|x| is not differentiable at x=0 so we can't differentiate it

Answer 4

then when is it differentiable?

Answer 5

thats what i ment to say @ash2326

Answer 6

It's differentiable everywhere except x=0

Answer 7

Got your point @UnkleRhaukus

Answer 8

However \( x|x| \) is differentiable at x=0

Answer 9

is it because at (0,0) it's no longer a curve but a point?

Answer 10

oh btw @ash2326 @UnkleRhaukus i was asking how to find the derivative lol

Answer 11

\[(\left| u \right|)'=\frac{u u'}{\left| u \right|}\]

Answer 12

@mukushla so (|f(x))' = \(\frac{f(x) f'(x)}{|f(x)|}?\)

Answer 13

yes
do u wanna prove it?

Answer 14

i dont think im in the mood for proving :p lol

Answer 15

see this
\[\frac{d}{dx} \left| u \right| = \frac{d}{dx}\sqrt{u^2} =\frac{d}{dx} (u^2)^{1/2}=\frac{1}{2} \ 2 u u' (u^2)^{-1/2}=\frac{u u'}{(u^2)^{1/2}}=\frac{u u'}{\left| u \right|}\]

Answer 16

lol why =_=