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abannavong

  • 3 years ago

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

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  1. abannavong
    • 3 years ago
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    y= abs(3x-1)

  2. phi
    • 3 years ago
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    when x > 1/3 this is the same as y= 3x-1 when x< 1/3 it is y= -3x+1

  3. abannavong
    • 3 years ago
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    so what rule can u use for the absolute value problems or can u do it on ur calculator

  4. abannavong
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    how would u use the power rule for the abs(3x-1)

  7. abannavong
    • 3 years ago
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    would u set (3x-1)^1 ?

  8. phi
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    and use the product rule?

  11. phi
    • 3 years ago
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    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
    • 3 years ago
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    First finish the first problem, then repost this quadratic, because it is more complicated, and might take time to explain

  13. abannavong
    • 3 years ago
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    kk

  14. TuringTest
    • 3 years ago
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    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
    • 3 years ago
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    can u differentiate it on your calculator?

  16. TuringTest
    • 3 years ago
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    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
    • 3 years ago
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    numbers*

  18. abannavong
    • 3 years ago
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    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
    • 3 years ago
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    I just showed you one way

  20. abannavong
    • 3 years ago
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    what r the other ways

  21. abannavong
    • 3 years ago
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    #stillconfused

  22. phi
    • 3 years ago
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    btw, turing I think you should tweak your rule to x dx/|x|

  23. L.T.
    • 3 years ago
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    @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
    • 3 years ago
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    oh ok thanks @L.T.

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