Mathematics 2007 JAMB Past Questions - Question 12: If y=x cos x,find dy/dx.

Correct Answer

D

Explanation

If y = cos x, find dy/dx, y = xcos xusing product rule dy/dx = cos x - x sin xTo find the derivative of y = x cos(x) with respect to x, we can use the product rule.The product rule states that if we have two functions u(x) and v(x), then the derivative of their product is given by:(d/dx)(u(x) * v(x)) = u'(x) * v(x) + u(x) * v'(x)In this case, u(x) = x and v(x) = cos(x).Taking the derivatives:u'(x) = 1 (the derivative of x with respect to x is 1)v'(x) = -sin(x) (the derivative of cos(x) with respect to x is -sin(x))Applying the product rule:dy/dx = u'(x) * v(x) + u(x) * v'(x)      = 1 * cos(x) + x * (-sin(x))      = cos(x) - x * sin(x)Therefore, the derivative of y = x cos(x) with respect to x is dy/dx = cos(x) - x * sin(x).