Can someone help me solve this? Let F(x)=f(f(x)) and G(x)=(F(x))^2 and suppose that f(3)=5,f(5)=2,f′(5)=15,f′(3)=15 Find F′(3) and G′(3).

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I solved F'(3) and got: F'(3) = f'(f(3)) * f'(3) = f'(5) * 15 = 15*15 = 225, this is right.

G'(3) is wrong though: G'(3) = 2F(3) + F'(3) = 22 + 225 = 229

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Answer 1 · 2018-02-10T18:53:20

# G'(3)=900#.

#G(x)=[F(x)]^2#.

#:. G'(x)=2F(x)*F'(x)=2f(f(x))*F'(x)#.

#:. G'(3)=2F(3)*F'(3)=2f(f(3))*225=450f(5)#.

#rArr G'(3)=450*2=900#.