Mathematics 2004 JAMB Past Questions - Question 37: If y=3 cos (x/3), find dy/dx when x=3π/2

Correct Answer

C

Explanation

To find dy/dx, we need to differentiate y = 3cos(x/3) with respect to x.Using the chain rule, we can differentiate y with respect to x as follows:dy/dx = d/dx [3cos(x/3)]To differentiate cos(x/3), we need to apply the chain rule. The derivative of cos(u) with respect to u is -sin(u), and the derivative of u = x/3 with respect to x is 1/3. Therefore, the derivative of cos(x/3) with respect to x is:d/dx [cos(x/3)] = -sin(x/3) * (1/3)Now, we can substitute this derivative into the expression for dy/dx:dy/dx = d/dx [3cos(x/3)] = 3 * (-sin(x/3) * (1/3))Simplifying further:dy/dx = -sin(x/3)Now, we can find dy/dx when x = 3π/2:dy/dx = -sin((3π/2)/3) = -sin(π/2) = -1Therefore, when x = 3π/2, dy/dx is equal to -1.