(A) Let $y = e^{-x}$.Using the chain rule for differentiation,we have:$\frac{dy}{dx} = \frac{d}{dx}(e^{-x})$Since the derivative of $e^u$ with respect

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(A) Let $y = e^{-x}$.Using the chain rule for differentiation,we have:$\frac{dy}{dx} = \frac{d}{dx}(e^{-x})$Since the derivative of $e^u$ with respect to $u$ is $e^u$,we apply the chain rule:$\frac{dy}{dx} = e^{-x} \cdot \frac{d}{dx}(-x)$$\frac{dy}{dx} = e^{-x} \cdot (-1)$$\frac{dy}{dx} = -e^{-x}$

Class 12 Mathematics Continuity and Differentiability Derivative at a point, Standard differentiation

Easy

Differentiate the following with respect to $x$: $e^{-x}$

A
$-e^{-x}$
B
$e^{-x}$
C
$-x e^{-x-1}$
D
$e^{x}$

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Derivative at a point, Standard differentiation

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Differentiate the following with respect to $x$: $e^{-x}$

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