Limits Continuity And Differentiability Question 87
Question: If $ f(0)=0,f’(0)=2 $ , then the derivative of $ y=f(f(f(f(x))) $ at $ x=0 $ is
Options:
A) 2
B) 8
C) 16
D) 4
Show Answer
Answer:
Correct Answer: C
Solution:
$ y’(x)=f’(f(f(f(x))))f’(f(f(x)))f’(f(x))f’(x) $
$ \Rightarrow 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 $ .
BETA
