Derivative of parametric equation (10points for quick answer)

If x=(t)+(1/t)
Y=(t)-(1/t)

Find dy/dx and d2y/dx2 in terms of parameter t

dx/dt = 1 - 1/t^2
dy/dx = 1 + 1/t^2

dy/dx = (dy/dr) ÷ (dy/dt) = (1 + 1/t^2)/(1 - 1/t^2) = (t^2 + 1)/(t^2 - 1)

d^2y/dt^2 = [(t^2 - 1) • 2t - (t^2 + 1) • 2t]/(t^2 - 1)^2 = (2t^3 - 2t - 2t^2 - 2t)/(t^2 - 1)^2 = -4t/(t^2 - 1)^2