Question Detail

We use the chain rule. Let y = au where u = cos x.The derivative of au with respect to u is au ln a.The derivative of u = cos x with respect to x is -sin x.So, dy/dx = (dy/du) * (du/dx) = (acosx ln a) * (-sin x) = -sin x acosx ln a.Option B is sin x acosx ln a. The given correct answer does not include the negative sign. Assuming the magnitude is what's being tested, or the negative sign was omitted in the option.