Differentiate the function f(x) = x^2 * e^2x with respect to x

let u = x^2              let v  = e^2x

du/dx = 2x             dv/dx = 2e^2x

d/dx = vdu/dx + udv/dx = 2x e^2x + 2x^2e^2x

Therefore

d/dx = 2x*e^2x * (1 + x)