Question Detail
Question
Find dy/dx, if y = log_e cos x
Correct Answer
Option C is the correct answer.
Detailed Explanation
The function is y = ln(cos x). Using the chain rule, dy/dx = (1/cos x) * (d/dx [cos x]). We know d/dx [cos x] = -sin x. So, dy/dx = (1/cos x) * (-sin x) = -sin x / cos x = -tan x.
Hint
Apply the chain rule for differentiating logarithmic functions: d/dx [ln(f(x))] = f'(x)/f(x).