abannavong Group Title calc help!!!! how do you differentiate absolute values?!?!??!?! one year ago one year ago

1. abannavong Group Title

y= abs(3x-1)

2. phi Group Title

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

3. abannavong Group Title

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

4. abannavong Group Title

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

5. phi Group Title

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)

6. abannavong Group Title

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

7. abannavong Group Title

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

8. phi Group Title

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?

9. abannavong Group Title

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?

10. abannavong Group Title

and use the product rule?

11. phi Group Title

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 - )

12. phi Group Title

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

13. abannavong Group Title

kk

14. TuringTest Group Title

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$\frac d{dx}\sqrt u=\frac{u'}{2\sqrt u}=\frac{2x}{2|x|}=\frac x{|x|}$

15. abannavong Group Title

can u differentiate it on your calculator?

16. TuringTest Group Title

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

17. TuringTest Group Title

numbers*

18. abannavong Group Title

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

19. TuringTest Group Title

I just showed you one way

20. abannavong Group Title

what r the other ways

21. abannavong Group Title

#stillconfused

22. phi Group Title

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

23. L.T. Group Title

@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

24. abannavong Group Title

oh ok thanks @L.T.