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MTH 102 Practice Questions MTH 102 Objective Question
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Question

Differentiate log_e(x²/(x³+5)) with respect to x
Options
A (10+2x³)/[x(x³+5)]
B (10+5x³)/[x(x³+5)]
C (10-x³)/[x(x³+5)]
Correct Answer
D -5x³/[x(x³+5)]
Correct Answer

Option C is the correct answer.

Detailed Explanation

Write ln(x²/(x³+5)) = 2lnx - ln(x³+5). Differentiating: 2/x - 3x²/(x³+5) = [2(x³+5)-3x³]/[x(x³+5)] = (10-x³)/[x(x³+5)].

Hint

Split the log of a quotient into a difference before differentiating.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 852 of 930
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