# 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?

Jan 14, 2017

$h ' \left(3\right) = 20$

#### Explanation:

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

$h ' \left(x\right) = 2 \left(f \left(x\right) + g \left(x\right)\right) \cdot \left(f ' \left(x\right) + g ' \left(x\right)\right)$

Therefore,

$h ' \left(3\right) = 2 \left(f \left(3\right) + g \left(3\right)\right) \cdot \left(f ' \left(3\right) + g ' \left(3\right)\right)$

$= 2 \left(2 + 0\right) \left(1 + 4\right) = 20$