Question Detail

MTH 102 Differentiation Objective Question
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Question

Find \( dy/dx \) for \( y = \ln(x \sin x) \).
Options
A \( (1/x) + \cot x \)
Correct Answer
B \( \cos x / (x \sin x) \)
C \( \ln(\sin x + x \cos x) \)
D \( (\sin x + x \cos x) / (x \sin x) \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

( y = \ln x + \ln(\sin x) ). Differentiating gives ( 1/x + \cot x ).

Hint

Use the property \( \ln(ab) = \ln a + \ln b \) to simplify before differentiating.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 143 of 930
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