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 find the derivative, we use the chain rule for natural logarithms: d/dx [ln(f(x))] = f'(x) / f(x).Here, f(x) = cos x.The derivative of f(x) is f'(x) = d/dx (cos x) = -sin x.Substitute these into the chain rule formula:dy/dx = (-sin x) / (cos x).Recall that sin x / cos x = tan x.So, dy/dx = -tan x. This matches option C.
Hint
Remember the chain rule for natural logarithms: d/dx [ln(f(x))] = f'(x) / f(x). Also, recall the derivative of cos x and the definition of tan x.