Mathematics 2010 JAMB Past Questions - Question 41: if y =xsinx, find dy/dx

Correct Answer

B

Explanation

if y = x sinx, thenLet u = x and v = sin xtherefore du/dx = 1 and dv/dx = cos xHence by the product rule,dy/dx = v du/dx + u dv/dx= (sin x) x 1 + x cos x= sin x + x cos xTo find dy/dx, the derivative of y with respect to x, we can use the product rule. Given y = x * sin(x), we can differentiate both sides of the equation with respect to x:dy/dx = d/dx(x * sin(x))Using the product rule, the derivative of the product of two functions u(x) and v(x) is given by:d(uv)/dx = u * dv/dx + v * du/dxIn this case, u(x) = x and v(x) = sin(x). Therefore, we have:dy/dx = x * d/dx(sin(x)) + sin(x) * d/dx(x)Now, let's differentiate each term separately:d/dx(sin(x)) = cos(x) (derivative of sin(x) is cos(x))d/dx(x) = 1 (derivative of x is 1)Substituting these derivatives back into the equation, we have:dy/dx = x * cos(x) + sin(x) * 1Simplifying further, we get:dy/dx = x * cos(x) + sin(x)Therefore, the derivative of y = x * sin(x) with respect to x is dy/dx = x * cos(x) + sin(x).