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If f(0)=0,f^(prime)(0)=2, then the deriv...

If `f(0)=0,f^(prime)(0)=2,` then the derivative of `y=f(f(f(x)))` at `x=0` is 2 (b) 8 (c) 16 (d) 4

A

2

B

8

C

16

D

4

Text Solution

Verified by Experts

`y'(x)=f'(f(f(f(x)))f'(f(f(x)))f'(f(x))f'(x)`
`therefore" "y'(0)=f'(f(f(f(0)))f'(f(f(0)))f'(f(0))f'(0)`
`=f'(f(f(0)))f'(f(0))f'(0)f'(0)`
`=f'(f(0))f'(0)f'(0)f '(0)`
`=f'(0)f'(0)f'(0)f'(0)`
`=(f'(0))^(4)=2^(4)=16`
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