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

Question

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

Accepted Answer

Given f(1) = 1, f'(1) = 3

Let y = f(f(f(x))) + (f(x))2

On differentiating both sides with respect to x we get,

$${{dy} \over {dx}}$$ = f'(f(f(x))).f'(f(x)).f'(x) + 2f(x).f'(x)

Now at x = 1,

$${{dy} \over {dx}}$$ = f'(f(f(1))).f'(f(1)).f'(1) + 2f(1).f'(1)

= f'(f(1)).f'(1).f'(1) + 2.1.f'(1)

= f'(1).f'(1).f'(1) + 2.1.f'(1)

= 3$$ \times $$3$$ \times $$3 + 2$$ \times $$3

= 33

Solutions · 1