MHT CET · Maths · Differentiation
If \(f(1)=1, f^{\prime}(1)=3\), then the derivative of \(f(f(f(x)))+(f(x))^2\) at \(x=1\) is
- A \(9\)
- B \(12\)
- C \(15\)
- D \(33\)
Answer & Solution
Correct Answer
(D) \(33\)
Step-by-step Solution
Detailed explanation
Let \(y = f(f(f(x))) + (f(x))^2\). \(\frac{dy}{dx} = f'(f(f(x))) \cdot f'(f(x)) \cdot f'(x) + 2f(x) \cdot f'(x)\)
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