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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 $x=6$ :

$F'(6) = f'(f(6))f'(6)$

$=f'(4)*10$

$=11*10$

$=110$

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

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

$=2*2*11*10$

$=440$