Question Detail

To find the derivative of y = acos x, we use the chain rule for exponential functions of the form d/dx (au) = au ln(a) (du/dx).Here, u = cos x, so du/dx = -sin x.Therefore, dy/dx = acos x ln(a) (-sin x) = -sin x acos x ln(a).Comparing this with the given options, option B is sin x acos x ln a. There appears to be a sign discrepancy in the provided correct option. Based on standard differentiation rules, the correct answer should be negative.