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A bunch of functions inside of functions

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Find $$f'(-1)$$, given $$f(y) = h(g(y)), h(2) = 55, g(-1) = 2, h'(2) = -1$$, and $$g'(-1) = 7$$.


    2. Relevant equations
    Maybe the chain rule?


    3. The attempt at a solution
    I thought that I could create a function given that $$g(-1)=2$$, so I thought maybe the function could be $$g(x)=-2x$$. But if I differentiate that, I get $$g'(x)=-2$$, and obviously that doesn't work since putting -1 into $$g'(x)=-2
    \\
    g'(-1)=-2≠7$$. I don't know what to do.
     
  2. jcsd
  3. Apr 2, 2013 #2

    CAF123

    User Avatar
    Gold Member

    Apply the chain rule to the function ##f(y) = h(g(y))##.
     
  4. Apr 2, 2013 #3

    Mark44

    Staff: Mentor

    And after you find f'(y), evaluate f'(-1).
     
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