Question Detail
Question
Find dy/dx if y = loge (cos x).
Correct Answer
Option C is the correct answer.
Detailed Explanation
To find dy/dx for y = loge (cos x), which is y = ln(cos x), we use the chain rule.The derivative of ln(u) is (1/u) * du/dx.Here, u = cos x.du/dx = d/dx(cos x) = -sin x.So, dy/dx = (1 / cos x) * (-sin x)= -sin x / cos xUsing the trigonometric identity tan x = sin x / cos x:dy/dx = -tan x.
Hint
Recall the chain rule for the derivative of a natural logarithm: d/dx(ln u) = (1/u) * du/dx. Also remember the derivative of cos x.