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Differentiable

  1. Sep 20, 2014 #1
    (a) State precisely the definition of: a function f is differentiable at a ∈ R.

    (b) Prove that, if f is differentiable at a, then f is continuous at a. You may
    assume that
    f '(a) = lim {f(x) - f(a)}/(x - a)
    x→a

    (c) Assume that a function f is differentiable at each x∈ R and also f(x) > 0
    for all x ∈R. Use the definition of the derivative and standard limit laws to
    calculate the derivative of:
    g(x) = (f(x))^0.25
    in terms of f(x) and f '(x).

    I did part a n b . But stuck at part c , can any1 guide me on part (c)?thank you
     
  2. jcsd
  3. Sep 20, 2014 #2

    mathman

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    Science Advisor
    Gold Member

    To save writing, let u = f(x). Therefore you want d/dx(u^0.25)={d/du(u^0.25)}{du/dx}=0.25u^(-0.75)u'.
     
  4. Sep 21, 2014 #3

    HallsofIvy

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    Staff Emeritus
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    This same question was posted in the "Calculus and Beyond Homework" section and answered there. Unusualsikill, do not post the same thing in more than one section. If a homework section is appropriate, post there only.
     
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