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Question

Let F(x)=f(f(x)) and G(x)=(F(x))^2
and suppose that f(6)=4, f(4)=2, f'(4)=11, f'(6)=10
Find
F'(6)=
G'(6)=

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Answer 1 · 2016-10-26T00:22:59

#F'(6) = 110#

#G'(6) = 440#

Apply the chain rule:

#F'(x) = d/dxf(f(x))#

#=f'(f(x))(d/dxf(x))#

#=f'(f(x))f'(x)#

#G'(x) = d/dx[F(x)]^2#

#2F(x)(d/dxF(x))#

#=2f(f(x))f'(f(x))f'(x)#

Substituting in #x=6#:

#F'(6) = f'(f(6))f'(6)#

#=f'(4)*10#

#=11*10#

#=110#

#G'(6) = 2f(f(6))f'(f(6))f'(6)#

#=2f(4)f'(4)*10#

#=2*2*11*10#

#=440#