Question Detail

MTH 102 Differentiation Objective Question
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Question

Find \( dy/dx \) for \( y = e^{-x} \sin 3x \).
Options
A \( e^{-x}(3\cos 3x - \sin 3x) \)
Correct Answer
B \( -e^{-x} \cos 3x \)
C \( 3e^{-x} \cos 3x \)
D \( e^{-x}(3\cos 3x + \sin 3x) \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Product rule: ( (-e^{-x})\sin 3x + e^{-x}(3\cos 3x) = e^{-x}(3\cos 3x - \sin 3x) ).

Hint

Recall the product rule and chain rule for each exponential and sine component.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 145 of 930
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