JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f (1) = 1, f ' (1) = 3\) , then the derivative of \(f\left( {f\left( {f\left( x \right)} \right)} \right) + \left( {f{{\left( x \right)}^2}} \right)\) at \(x = 1\) is
- A \(33\)
- B \(15\)
- C \(9\)
- D \(12\)
Answer & Solution
Correct Answer
(A) \(33\)
Step-by-step Solution
Detailed explanation
\(f = f\left( {f\left( {f\left( x \right)} \right)} \right) + {\left( {f\left( x \right)} \right)^2}\) \(\frac{{dy}}{{dx}} = f'\left( {f\left( {f\left( x \right)} \right)} \right)f'\left( {f\left( x \right)} \right)f'\left( x \right) + 2f\left( x \right)f'\left( x \right)\) Put…
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