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Suppose that f(0)=0a n df^(prime)(0)=2, ...

Suppose that `f(0)=0a n df^(prime)(0)=2,` and let `g(x)=f(-x+f(f(x)))dot` The value of `g'` (0) is equal to _____

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`g(x)=f(-x+f(f(x))), f(0)=0, f'(0)=2`
`g'(x)=f'(-x+f(f(x)))cdot[-1+f'(f(x))cdotf'(x)]`
`g'(0)=f'(f(0))cdot[-1+f'(0)cdotf'(0)]`
`=f'(0)[-1+(2)(2)]=(2)(3)=6`
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CENGAGE-DIFFERENTIATION-Exercise (Numerical)
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