If f(x) and g(x) are functions such that $f(3)=2, f'(3)=1,g(3)=0,$ and $g'(3)=4$ . What is $h'(3)$ , where $h(x)= (f(x) +g(x))^2$ ?

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Answer 1 · 2017-01-14T16:35:48

$h'(3) = 20$

Since $h(x)=(f(x)+g(x))^{2}$ , the Chain Rule and Linearity of the derivative operator imply that

$h'(x)=2(f(x)+g(x))*(f'(x)+g'(x))$

Therefore,

$h'(3)=2(f(3)+g(3))*(f'(3)+g'(3))$

$=2(2+0)(1+4)=20$

If f(x) and g(x) are functions such that f(3)=2, f'(3)=1,g(3)=0,f(3)=2, f'(3)=1,g(3)=0, and g'(3)=4g'(3)=4. What is h'(3)h'(3), where h(x)= (f(x) +g(x))^2h(x)= (f(x) +g(x))^2?