## 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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1. Empty

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

2. 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

3. 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 $$H'$$.