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MTH 102 Practice Questions MTH 102 Objective Question
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Question

Differentiate e^(2x)/(2x-3)²
Options
A e^(2x)(2x-5)/(2x-3)³
B (2x-5)/(2x-3)³
C 2e^(2x)(2x-5)/(2x-3)³
Correct Answer
D 2e^(2x)/(2x-3)⁴
Correct Answer

Option C is the correct answer.

Detailed Explanation

By the quotient rule: [(2x-3)²(2e^(2x)) - e^(2x)(2)(2x-3)(2)]/(2x-3)⁴. Factoring out (2x-3) from top and bottom leaves 2e^(2x)[(2x-3)-2]/(2x-3)³ = 2e^(2x)(2x-5)/(2x-3)³.

Hint

Use the quotient rule, then factor a common (2x-3) out of the numerator to simplify the power in the denominator.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 825 of 930
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