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GATE 2022 CH – Question 13

Engineering Mathematics · Calculus: Limits, continuity, differentiability, Taylor series and mean value theorem · 1 mark · Multiple choice

Let $f(x) = e^{-|x|}$, where $x$ is real. The value of $\frac{df}{dx}$ at $x = -1$ is

  1. $-e$
  2. $e$
  3. $1/e$
  4. $-1/e$

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Correct answer: (C) $1/e$

Explanation

For $x < 0$, $|x| = -x$ and $f(x) = e^{x}$, so $\frac{df}{dx} = e^{x}$ and at $x = -1$ it equals $e^{-1} = \frac{1}{e}$.