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
explanation: The document is a forum thread discussing a math problem involving the chain rule for derivatives. The user posts a question about finding the first derivative of a composition of functions and provides their attempt at solving it. Another user responds by pointing out errors in the derivatives of \( g(x) \) and \( h(x) \) and provides the correct derivatives. The thread contains a question and a partial answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread discussing a math problem involving the chain rule for derivatives. The user posts a question about finding the first derivative of a composition of functions and provides their attempt at solving it. Another user responds by pointing out errors in the derivatives of \( g(x) \) and \( h(x) \) and provides the correct derivatives. The thread contains a question and a partial answer.
  
  Label: question-and-answer