Let F(x)=f(f(x)) and G(x)=(F(x))^2. You also know that f(8)=4, f(4)=3, f'(4)=3, f'(8)=6. Find F'(8) and G'(8)

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cosinusix | College Teacher | (Level 3) Assistant Educator

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The derivative `f(f(x))'=f'(x)*f'(f(x))`

`F'(8)=f'(8)*f'(f(8))=6*f'(4) ` because `f'(8)=6` and `f(8)=4`

`F'(8)=6*3=18`

 

`G'(x)=2F'(x)F(x)`

 

`G'(8)=2F'(8)F(8) `

 

`F'(8)=18`

`F(8)=f(f(8))=f(4)=3`

`G'(8)=2*18*3=108`

 

Solution: `F'(8)=18` and `G'(8)=108`

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