Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Given the function y = cot(5x²+3), find dy/dx.
Options
A −10x cosec²(5x²+3)
Correct Answer
B −10x cosec(5x²+3)cot(5x²+3)
C 10x cosec²(5x²+3)
D −10x cot(5x²+3)
Correct Answer

Option A is the correct answer.

Detailed Explanation

To differentiate y = cot(5x²+3), use the chain rule. The derivative of cot(u) is -cosec²(u) * (du/dx).Let u = 5x²+3.Then, du/dx = d/dx (5x²+3) = 10x.Substitute these into the chain rule formula:dy/dx = -cosec²(u) * (du/dx) = -cosec²(5x²+3) * (10x).Rearranging, dy/dx = -10x cosec²(5x²+3).Option A matches this result.

Hint

Remember the derivative of cot(u) is -cosec²(u) and apply the chain rule.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 392 of 930
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