Question:
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?
\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?
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Shortcut: \((e^{kx})'=k\,e^{kx}\).
Updated On: Oct 17, 2025
- \(\dfrac{e^{-3x}}{3}\)
- \(\dfrac{e^{-3x}}{-3}\)
- \(3e^{-3x}\)
- \(-3e^{-3x}\)
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The Correct Option is D
Solution and Explanation
Idea. Derivative of \(e^{u}\) is \(e^{u}\cdot u'\). Here \(u=-3x\) so \(u'=-3\).
\[ \frac{d}{dx}e^{-3x}=e^{-3x}\cdot(-3)=-3e^{-3x}. \]
\[ \frac{d}{dx}e^{-3x}=e^{-3x}\cdot(-3)=-3e^{-3x}. \]
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