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). Using the chain rule, the derivative of ln(u) is (1/u) * du/dx. Here, u = cos x, so du/dx = -sin x. Therefore, dy/dx = (1/cos x) * (-sin x) = -sin x / cos x = -tan x.
Hint
Recall the derivative of ln(u) and apply the chain rule, where u is cos x.