Partial differentiation, chain rule help..?

the function f(x, y)= x^3 + x^2y + y^2 +2y.



Use the chain rule to determine, in terms of t, the rate of change of f with

time along the path given at time t by x(t)=鈭?1+ t^2, y(t)= 鈭抰. (x(t)=sqrt 1+t^2)



can any one show me how its done step by step please, thank you.Partial differentiation, chain rule help..?
f(x,y) = x鲁 + x虏y + y虏 + 2y

x = 鈭?1+ t虏) ; y = -t



df/dt = 鈭俧/鈭倄 dx/dt + 鈭俧/鈭倅 dy/dt .................... f' = 鈭噁 鈭?(x',y')

= (3x虏 + 2xy) t/鈭?1+ t虏) - (x虏 + 2y + 2)

= (3(鈭?1+ t虏))虏 - 2t(鈭?1+ t虏))) t/鈭?1+ t虏) - ((鈭?1+ t虏))虏 - 2t + 2)

= t(3鈭?1+ t虏) - 3t + 2) - 3



Answer: df/dt = t(3鈭?1+ t虏) - 3t + 2) - 3