JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) be a differentiable function such that \(f(1) = 2\) and \(f\,'(x) = f(x)\) for all \(x\in R.\) If \(h(x) = f(f(x)),\) then \(h'(1)\) is equal to
- A \(2e^2\)
- B \(4e\)
- C \(2e\)
- D \(4e^2\)
Answer & Solution
Correct Answer
(B) \(4e\)
Step-by-step Solution
Detailed explanation
\(\frac{{f'\left( x \right)}}{{f\left( x \right)}} = 1\,\,\,\forall x \in R\) Integrate and use \(f\left( 1 \right) = 2\) \(f\left( x \right) = 2{e^{x - 1}} \Rightarrow f'\left( x \right) = 2{e^{x - 1}}\)…
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