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    How do you find a derivative when part of the function is in absolute value?
    ex-
    f(x)= 3(x-1)^(2/3) +|2x-1|
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    If x is not 1/2, you can rewrite this without the absolute value (i.e. if x > 1/2, |2x-1| = 2x-1, if x < 1/2, |2x-1| = 1-2x).

    f is not going to be differentiable at x = 1/2. (think of the shape of |2x-1| near x=1/2).
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    (Original post by PatchworkTeapot)
    How do you find a derivative when part of the function is in absolute value?
    ex-
    f(x)= 3(x-1)^(2/3) +|2x-1|
    d/dx|x| = sgn(x), x cannot be zero
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    (Original post by DFranklin)
    If x is not 1/2, you can rewrite this without the absolute value (i.e. if x > 1/2, |2x-1| = 2x-1, if x < 1/2, |2x-1| = 1-2x).

    f is not going to be differentiable at x = 1/2. (think of the shape of |2x-1| near x=1/2).
    That makes sense,but how would you come up with an overall derivative for this function, taking the 2 cases into account?
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    (Original post by PatchworkTeapot)
    That makes sense,but how would you come up with an overall derivative for this function, taking the 2 cases into account?
    I'd just write the two cases.

    If you really want to do it in one go, you can write the derivative of |x| as x / |x| (note it's still indeterminate at x = 0). Similarly for derivative of |ax-b| etc...
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    (Original post by PatchworkTeapot)
    That makes sense,but how would you come up with an overall derivative for this function, taking the 2 cases into account?
    What's wrong with a piecewise-defined function?
 
 
 
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