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Derivatives of Composite Functions

  1. Oct 24, 2005 #1
    I just need a nudge in the rigth direction ais dont know where to start
    Let y = f(x^2 + 3x - 5) find dy/dx when x = 1, given that f'(-1) = 2

  2. jcsd
  3. Oct 24, 2005 #2


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    Let g(x) = x² + 3x - 5, then y = f(g(x)). dy/dx = f'(g(x))g'(x)
  4. Oct 24, 2005 #3
    i am not sure what else y have to do to get the answer, i wrote that out as well as

    -1 = x^2 + 3x -5
    solved and got x = 1 or -3...

    but what else?

    dy/dx = f'(x^2 + 3x - 5)(2x + 3)
  5. Oct 24, 2005 #4


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    I suggest going back and reading the problem again! You were asked to find y'(1). How about setting x= 1?
  6. Oct 24, 2005 #5
    Very good suggestion.

    And just to ease your worries, you were given a good piece of information: that f'(-1)=2. Do you see where this applies to the problem?
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