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Question:

If f(1)=1, f'(1)=3, then the value of derivative of f(f(f(x)))+(f(x))^2 at x=1 is?

9

20

33

12

Solution:

The correct option is B
33
y=f(f(f(x)))+(f(x))^2
dy/dx=f'(f(f(x)))*f'(f(x))*f'(x)+2f(x)f'(x)
Put x=1 ⇒f'(f(f(1)))*f'(f(1))*f'(1)+2f(1)*f'(1)=27+6=33.