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Let $f$ be a differentiable function such that $f(1) = 2$ and $f’(x) = f(x)$ for all $x \in \mathbb{R}$. If $h(x) = f(f(x))$, then $h’(1)$ is equal to:
(1) $2e^2$
(2) $4e$
(3) $2e$
(4) $4e^2$
Type: MCQ
$f(x) = \frac{2}{e} e^x$, $h’(1) = f’(f(1)) \cdot f’(1) = f’(2) \cdot f’(1) = \frac{2}{e}e^2 \cdot \frac{2}{e} \cdot e = 4e$
BETA
