Question Detail
Question
Find dy/dx if y = loge(cos x).
Correct Answer
Option C is the correct answer.
Detailed Explanation
Given y = loge(cos x), which is equivalent to y = ln(cos x).Using the chain rule for logarithms, d/dx [ln(u)] = u'/u.Here, u = cos x, so u' = d/dx (cos x) = -sin x.Therefore, dy/dx = (-sin x) / (cos x) = -tan x.
Hint
Recall that loge(u) is the same as ln(u). Apply the chain rule: d/dx ln(f(x)) = f'(x)/f(x).