Differentiate the functions $e^{-x}$ wit

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Target Exam

CUET

Subject

Maths. Section B1

Chapter

Continuity and Differentiability

Question:

Differentiate the functions $e^{-x}$ with respect to $x$.

Options:

$e^{-x}$

$-e^{-x}$

$xe^{-x}$

$-e^{x}$

Correct Answer:

$-e^{-x}$

Explanation:

The correct answer is Option (2) → $-e^{-x}$ ##

Let $y = e^{-x}$.

Using chain rule, we have

$\frac{dy}{dx} = e^{-x} \cdot \frac{d}{dx}(-x) = -e^{-x}$