calc help!!!! how do you differentiate absolute values?!?!??!?!

- anonymous

calc help!!!! how do you differentiate absolute values?!?!??!?!

- jamiebookeater

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- anonymous

y= abs(3x-1)

- phi

when x > 1/3 this is the same as y= 3x-1
when x< 1/3 it is y= -3x+1

- anonymous

so what rule can u use for the absolute value problems or can u do it on ur calculator

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- anonymous

bc i know you cant use the product rule or the quotient rule or the power rule it seems like or the chain rule

- phi

one other thing, dy/dx is undefined at x= 1/3
use the power rule
d/dx a x^n = a n x^(n-1)

- anonymous

how would u use the power rule for the abs(3x-1)

- anonymous

would u set (3x-1)^1 ?

- phi

you get 3 different answers, depending on x
x> 1/3 d/dx (y= 3x-1)
x= 1/3 undefined
x<1/3 d/dx (y= -3x+1)
d/dx y = dy/dx
d/dx (3x^1 - 1) = d/dx 3x^1 + d/dx (-1)
can you finish?

- anonymous

yeah now i can oh ok and also i have another question for absolute values differentiate y= abs(x^2-5x+4) would u jst factor it out first?

- anonymous

and use the product rule?

- phi

for abs(x^2-5x+4)
you have to find the values of x where this stays positive
and the regions where it is negative (then replace abs with - )

- phi

First finish the first problem, then repost this quadratic, because it is more complicated, and might take time to explain

- anonymous

kk

- TuringTest

if I may add, one trick to differentiating absolute value can be to use the definition\[|x|=\sqrt{x^2}\]let\[u=x^2\]then\[\frac d{dx}\sqrt u=\frac{u'}{2\sqrt u}=\frac{2x}{2|x|}=\frac x{|x|}\]

- anonymous

can u differentiate it on your calculator?

- TuringTest

I rely on my brain for differentiation usually, I've lost track of what handheld calculators are good for besides graphing and handling ugly nmbers

- TuringTest

numbers*

- anonymous

i dont think my teacher has taught us how to differentiate absolute values yet but she assigned us an assignment with like 2 absolute value problems im still a bit confused on how to differentiate it

- TuringTest

I just showed you one way

- anonymous

what r the other ways

- anonymous

#stillconfused

- phi

btw, turing I think you should tweak your rule to x dx/|x|

- anonymous

@abannavong, another way to find the derivative is to set up the difference quotient and multiply by the conjugate of the numerator
(|x+h|-|x|)/h-->((|x+h|-|x|)(|x+h|+|x|))/(h*(|x+h|+|x|))
Hint: When you square an absolute value, you can drop the absolute value signs

- anonymous

oh ok thanks @L.T.

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