Question

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)=?

Answer 1

Do your best, start out by using the chain rule and take the derivative of H(x)

Answer 2

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

Answer 3

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 \(H'\).