anonymous
  • anonymous
suppose f(5)=3 f '(5)=3 f(26)=3 f '(26)=7 g(5)=1 g '(5)=-2 and H(x)=f(x^2+g(x)) find dH/dx x=5 H '(5)=?
Mathematics
katieb
  • katieb
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Empty
  • Empty
Do your best, start out by using the chain rule and take the derivative of H(x)
anonymous
  • anonymous
I don't know how to do any of that, it's for an online class and my teacher only posts vague notes and no examples
anonymous
  • anonymous
Let's say you have a function \(r(x)=s(t(x))\). By the chain rule, the derivative of \(r\) with respect to \(x\) is given by \[r'(x)=s'(t(x))\times t'(x)\] In your question, you have a function \(H(x)=f(x^2+g(x))\). Let \(s(x)=f(x)\) and \(t(x)=x^2+g(x)\). Then \(r(x)=s(t(x))=H(x)\). By the chain rule, \[H'(x)=f'(x^2+g(x))\times (x^2+g(x))'=f'(x^2+g(x))\times(2x+g'(x))\] The idea now is to use what info you know about particular values of \(f,g,f',g'\) to determine the particular value of \(H'\).

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