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Given values, find derivatives

  1. Oct 17, 2006 #1
    Given y = f(x) with f(1) = 4 and f'(1) = 3, find

    (a) [tex] g'(1) if g(x) = \sqrt {f(x)} [/tex]
    (b) [tex] h'(1) if h(x) = f(\sqrt {x}) [/tex]

    (a) [tex] g'(x) = \frac {1}{2} f(x)^\frac{-1}{2} * f'(x) [/tex]
    [tex] g'(1) = \frac {1}{2} f(1)^\frac{-1}{2} * f'(1) [/tex]
    [tex] g'(1) = \frac {1}{2}(4)^\frac{-1}{2} * 3 [/tex]
    [tex] g'(1) = \frac {3}{4} [/tex]

    (b) [tex] h'(x) = f'(\sqrt{x}) [/tex]
    [tex]h'(1) = f'(\sqrt{1}) [/tex]
    [tex]h'(1) = f'(1) [/tex]
    [tex]h'(1) = 3 [/tex]

    Are these correct?

    I'm not sure if this was the correct approach.

    Thanks.
     
    Last edited: Oct 17, 2006
  2. jcsd
  3. Oct 17, 2006 #2
    (a) correct


    (b) If [tex] h(x) = f(\sqrt{x}) [/tex], then [tex] h'(x) = f'(\sqrt{x})\frac{1}{2}x^{-\frac{1}{2}} [/tex]. So it should be [tex] \frac{3}{2}[/tex]
     
    Last edited: Oct 17, 2006
  4. Oct 17, 2006 #3
    thanks, just a simple mistake :redface:
     
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