Question

\(\dfrac{d}{dx}\left(e^{-3x}\right)=\) ?

• A. \(\dfrac{e^{-3x}}{3}\)
• B. \(\dfrac{e^{-3x}}{-3}\)
• C. \(3e^{-3x}\)
• D. \(-3e^{-3x}\)

Hint:

Shortcut: \((e^{kx})'=k\,e^{kx}\).

Answer 1

The Correct Option is D

Idea. Derivative of \(e^{u}\) is \(e^{u}\cdot u'\). Here \(u=-3x\) so \(u'=-3\).
\[ \frac{d}{dx}e^{-3x}=e^{-3x}\cdot(-3)=-3e^{-3x}. \]