Mathematics 2000 JAMB Past Questions - Question 36: If y=2x cos 2x-sin 2x, find dy/dx when x=π/4

Correct Answer

B

Explanation

Find the value of ∫λ /0 (cos²ѳ-1/sin² ѳ)dѳ Find the value of ∫λ /0 (cos²ѳ-1/sin² ѳ)dѳ To find dy/dx, we need to differentiate the given function y = 2x cos(2x) - sin(2x) with respect to x.Using the product rule and chain rule, we can differentiate each term separately.Let's start with the first term: 2x cos(2x).Using the product rule, we have:d/dx (2x cos(2x)) = 2 cos(2x) + 2x (-sin(2x))(2)Simplifying this, we get:d/dx (2x cos(2x)) = 2 cos(2x) - 4x sin(2x)Now, let's differentiate the second term: -sin(2x).Using the chain rule, we have:d/dx (-sin(2x)) = -cos(2x)(2)Simplifying this, we get:d/dx (-sin(2x)) = -2cos(2x)Now, let's differentiate the entire function y = 2x cos(2x) - sin(2x) by adding the derivatives of each term:dy/dx = (2 cos(2x) - 4x sin(2x)) - 2cos(2x)Simplifying this, we get:dy/dx = -4x sin(2x)Now, we can substitute x = π/4 into the expression to find the value of dy/dx:dy/dx = -4(π/4) sin(2(π/4))      = -π sin(π/2)      = -πTherefore, when x = π/4, the value of dy/dx is -π.