Question Detail

Given y = loge cos x, which is equivalent to y = ln(cos x).To find dy/dx, we use the chain rule for derivatives.The derivative of ln(u) is (1/u) * u'.Here, u = cos x.So, u' = 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 xTherefore, the correct option is C.