Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

The second derivative of 3 sin 2x is
Options
A -12 sin 2x
Correct Answer
B 6 sin 2x
C 6 cos 2x
D 12 cos 2x
Correct Answer

Option A is the correct answer.

Detailed Explanation

Let y = 3 sin 2x.1. Find the first derivative (y'): y' = d/dx (3 sin 2x) = 3 * (cos 2x) * (d/dx(2x)) (using chain rule) y' = 3 * cos 2x * 2 = 6 cos 2x2. Find the second derivative (y''): y'' = d/dx (6 cos 2x) = 6 * (-sin 2x) * (d/dx(2x)) (using chain rule) y'' = 6 * (-sin 2x) * 2 = -12 sin 2x

Hint

Apply the chain rule twice for the derivatives of trigonometric functions.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 299 of 930
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