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MTH 102 Practice Questions MTH 102 Objective Question
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Question

Obtain Δy/Δx of the derivative of y=sec(x) using first principle
Options
A [2cos((2x+Δx)/2)sin(Δx/2)]/[Δx cos(x+Δx)cos(Δx)]
B [2sin((2x+Δx)/2)cos(Δx/2)]/[Δx cos(x+Δx)cos(Δx)]
C [-2sin((2x+Δx)/2)sin(Δx/2)]/[sin(x+Δx)cos(Δx)]
D [-2sin((2x+Δx)/2)sin(Δx/2)]/[Δx cos(x+Δx)cos(Δx)]
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

Δy/Δx = [sec(x+Δx)-secx]/Δx = [cosx-cos(x+Δx)]/[Δx cos(x+Δx)cosx]. Applying the sum-to-product formula to the numerator gives the form in option D.

Hint

Write sec as 1/cos, combine into a single fraction, then use the sum-to-product identity on the resulting cosine difference.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 928 of 930
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