Hi. Given a one-parameter family of maps such as(adsbygoogle = window.adsbygoogle || []).push({});

Φ_{t}: ( x , y ) → ( xe^{t}+ 2e^{t}-2 , ye^{2t}) the velocity vector field at t=0 is given by d(Φ_{t})/dt = (x+2) ∂/∂x + 2y ∂/∂y

My question is ; how does differentiating a vector function Φ_{t}with respect to t result in a scalar function ? Thanks

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# I Velocity vector fields

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