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 = loge(cos x), which is equivalent to y = ln(cos x).To differentiate, use the chain rule: d/dx(ln(f(x))) = 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) = -tan x.
Hint
Remember that loge is the natural logarithm, ln, and apply the chain rule.