Question Detail
Question
Find dy⁄dx, if y = loge cos x
Correct Answer
Option C is the correct answer.
Detailed Explanation
To find the derivative of y = loge(cos x), which is ln(cos x), we apply the chain rule. The derivative of ln(u) is (1⁄u) * du⁄dx. Here, u = cos x, so du⁄dx = -sin x. Therefore, dy⁄dx = (1⁄cos x) * (-sin x) = -sin x ⁄ cos x = -tan x.
Hint
Apply the chain rule for derivatives of logarithmic functions.