The equation of a curve is given by

\(y=xe^{-2x}.\)

(i) Find \(\frac{dy}{dx}\).

(ii) Find the exact coordinates of the stationary point on the curve \(y=xe^{-2x}\).

(iii) Find, in terms of \(e\), the equation of the tangent to the curve \(y=xe^{-2x}\) at the point \(\left(1,\frac1{e^2}\right)\).

(iv) Using your answer to part (i), find \(\int xe^{-2x}\,dx\).