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).To differentiate y with respect to x, we use the chain rule, where d/dx(ln(u)) = (1/u) du/dx.Here, u = cos x.So, du/dx = d/dx(cos x) = -sin x.Therefore,dy/dx = (1 / cos x) * (-sin x)dy/dx = -sin x / cos xSince sin x / cos x = tan x, we have:dy/dx = -tan xThis matches option C.
Hint
Recall the derivative rule for ln(u) and the derivative of cos x.