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If f(1) = 1, f'(1) = 3, then the de...

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

A

15

B

12

C

9

D

33

Text Solution

Verified by Experts

` y = f (f (f (x)))+ (f(x))^2 `
` (dy ) /(dx) = f' ( f ( f (x))).f' (f (x) ).f' (x) + 2 f (x) f' (x ) `
put ` x = 1 rArr f'(f(f(1))).f'(f(1)).f'(1) + 2 f(1).f'(1)=27 + 6 = 33 `
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