Mathematics 2008 JAMB Past Questions - Question 37: Differentiate sin x-xcos x.

Correct Answer

B

Explanation

y = sin x - x cos xlet U = - x, dy/dx = -1, V cos x, dx/dx = -5x-x (-sin x) + cos x (-1)dy/dx = sin x cos x - cos xTo differentiate the function f(x) = sin(x) - xcos(x), we can use the product rule and the chain rule.The product rule states that if we have a function of the form f(x) = g(x) * h(x), then the derivative of f(x) is given by:f'(x) = g'(x) * h(x) + g(x) * h'(x)Applying the product rule to the given function f(x) = sin(x) - xcos(x), we have:f'(x) = (cos(x) - cos(x) + xsin(x))Simplifying further:f'(x) = xsin(x)Therefore, the derivative of sin(x) - xcos(x) is xsin(x).dy/dx = x sin x