First slide
Derivatives
Question

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

Moderate
Solution

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)2=f(f(0))f(0)f(o)2=f(0)2.22=2.2.2.2=16

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