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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#?

1 Answer

Jan 14, 2017

#h'(3) = 20#

Explanation:

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#

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