AP EAMCET · Maths · Differentiation
If \(f(0)=0, f^{\prime}(0)=3\), then the derivative of \(y=f(f(f(f(f(x)))))\) at \(x=0\) is
- A 16
- B 32
- C 81
- D 243
Answer & Solution
Correct Answer
(D) 243
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(0)=0, f^{\prime}(0)=3 \\ & y=f(f(f(f(f(x))))) \\ & \frac{d y}{d x}=f^{\prime}(f(f(f(f(x))))) f^{\prime}(f(f(f(x))))\end{aligned}\) \(f^{\prime}(f(f(x))) f^{\prime}(f(x)) f^{\prime}(x)\)…
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