Partial Differentiation

If z=xe^y + ysinx , x=t and y=t^2
z = (t)e^(t^2) + (t^2)sin(t)
dz/dt = { (t)' e^(t^2) + t [e^(t^2)]' } + { (t^2)' sin(t) + (t^2) [sin(t)]' }
dz/dt = e^(t^2)+ t ‧ 2t ‧ e^(t^2) + 2t sin(t) + (t^2) cos(t)
dz/dt = e^(t^2)+ 2(t^2) e^(t^2) + 2t sin(t) + (t^2) cos(t)
dz/dt = [1+2(t^2)] e^(t^2) + 2t sin(t) + (t^2) cos(t)

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