Question Detail
Question
Find dy/dx if y = loge(cos x).
Correct Answer
Option C is the correct answer.
Detailed Explanation
The function is y = ln(cos x).To differentiate y = ln(f(x)), we use the chain rule: dy/dx = f'(x)⁄f(x).Here, f(x) = cos x.So, f'(x) = d/dx(cos x) = -sin x.Therefore, dy/dx = (-sin x)⁄(cos x).Since sin x⁄cos x = tan x, we have:dy/dx = -tan x.This matches option C.
Hint
Remember the derivative of ln(f(x)) and the derivative of cos x. Use the identity sin x / cos x = tan x.