derivative of U(X(t),t) with respect to t

[forget_f1]

What is the derivative of U(X(t),t)?

Is it Ut(Xt(t),t)?

[HallsofIvy]

In general, the derivative of U(x,y) with respect to t is, by the chain rule,
Ux(x,y)xt+ Uy(x,y)yt.

Notice that the derivatives of x and y are multiplied by U(x,y), not arguments in it!

In the case that y= t, that reduces to
Ux(x,y)(xt)+ Ut.