Mathematics 2001 JAMB Past Questions - Question 34: If y=x sin x ,find dy/dx when x=π/2

Correct Answer

B

Explanation

To find dy/dx, we need to differentiate the function y = x sin(x) with respect to x.Using the product rule, the derivative of y = x sin(x) is given by:dy/dx = x * d(sin(x))/dx + sin(x) * d(x)/dxThe derivative of sin(x) with respect to x is cos(x), and the derivative of x with respect to x is 1.Substituting these derivatives into the equation, we have:dy/dx = x * cos(x) + sin(x) * 1Now, let's evaluate dy/dx when x = π/2:dy/dx = (π/2) * cos(π/2) + sin(π/2) * 1cos(π/2) = 0 and sin(π/2) = 1, so we have:dy/dx = (π/2) * 0 + 1 * 1dy/dx = 0 + 1dy/dx = 1Therefore, when x = π/2, the value of dy/dx is 1.