text: # Thread: Derivative, Chain Rule Problem. Help Plz!!
  
  1. ## Derivative, Chain Rule Problem. Help Plz!!
  
  The question is asking to find the first derivative of the composition (fogoh)(x). Given:
  
  $\displaystyle f(x) = \sqrt{x^2-1}$
  $\displaystyle g(x) = (x^3+5)^{17}$
  $\displaystyle h(x) = \frac{2}{x}$
  
  Computing for the derivatives I got:
  
  $\displaystyle f'(x) = \tfrac{1}{2}(x^2-1)^{\frac{-1}{2}}(2x)$
  $\displaystyle g'(x) = 17{(x^3+5)}^{16}(3x)$
  $\displaystyle h'(x) = -2(2x)$
  
  I understand that the derivative of $\displaystyle f(g(h(x))) = [f'(g(h(x)))].[g'(h(x))].[h'(x)]$ so I just need to plug the functions but I am not getting the right answer. Can someone please take me through the process step by step so I can see where I went wrong? I understand this is a long question but it would be greatly appreciated! Thank you!
  
  2. f ' is correct but g ' and but h ' aren't
  
  g= (x^3 + 5)^17
  
  g ' = 17(x^3 +5)^16 (3x^2)
  
  h = 2/x = 2x^(-1)
  
  h' = -2 x^(-2) = -2/(x^2)
  
  Try it now