Question Detail
Question
Find dy/dx if y = loge cos x
Correct Answer
Option C is the correct answer.
Detailed Explanation
The function given is y = loge cos x, which can also be written as y = ln(cos x). To find the derivative dy/dx, we use the chain rule. The derivative of ln(f(x)) is f'(x)/f(x). Here, f(x) = cos x, so f'(x) = -sin x. Therefore, dy/dx = (-sin x) / (cos x) = -tan x.
Hint
Recall the derivative of ln(u) and apply the chain rule.