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Question

If f(0)=0, f(0)=2 then the derivative of y=f(f(f(f(x)))) at x=0 is

A
2
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B
8
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C
16
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D
4
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Solution

The correct option is C 16
y=f(f(f(f(x))))
Thus using chain rule
y(x)=f(f(f(f(x)))).f(f(f(x))).f(f(x)).f(x)
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(0))4=24=16

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