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anonymous
 one year ago
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)=?
anonymous
 one year ago
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)=?

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Empty
 one year ago
Best ResponseYou've already chosen the best response.0Do your best, start out by using the chain rule and take the derivative of H(x)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0Let'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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