Question Detail

To find the derivative of y = logₑ(cos x), also written as y = ln(cos x), we use the chain rule.The derivative of ln(f(x)) is f'(x) / f(x).Here, f(x) = cos x.So, f'(x) = d/dx(cos x) = -sin x.Therefore, dy/dx = (-sin x) / (cos x).Since sin x / cos x = tan x, we have:dy/dx = -tan x.Thus, option C is correct.