Question:
If \( y = e^{-2x} \), then \( \frac{d^3y}{dx^3} \) is equal to:
If \( y = e^{-2x} \), then \( \frac{d^3y}{dx^3} \) is equal to:
Show Hint
When differentiating exponential functions of the form \( e^{ax} \), apply the chain rule repeatedly.
Updated On: June 02, 2025
- \( 2e^{-2x} \)
- \( e^{-4x} \)
- \( 4e^{-4x} \)
- \( -8e^{-2x} \)
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The Correct Option is D
Solution and Explanation
Step 1: Differentiate \( y = e^{-2x} \):
\[
\frac{dy}{dx} = -2e^{-2x}.
\]
Step 2: Differentiate again:
\[
\frac{d^2y}{dx^2} = 4e^{-2x}.
\]
Step 3: Differentiate once more:
\[
\frac{d^3y}{dx^3} = -8e^{-2x}.
\]
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