What is the derivative of y = sec(x) with respect to x?
Answer and explanation
Correct answer: C. sec x tan x
- Step 1: sec(x) = 1 / cos(x) = (cos x)^(-1). Step 2. By chain rule, - (cos x)^(-2) (-sin x) = sin x / cos^2 x = (1/cos x)(sin x/cos x) = sec x tan x. Answer: sec x tan x. Why not the others:* sec^2 x is the derivative of tan x; tan^2 x is not a derivative of sec x; -sec x tan x has an incorrect minus sign.
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