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This is 6 questions, but ok For the sake of simplicity I'm going to change the notation and say u = u(x,y), v = v(x,y), and u and v are differentiable.

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I have two functions x = x(u,v) and y = y(u,v) The chain rule says that for a function f(x,y), df/dx = df/du du/dx df/dv dv/dx, and similarly df/dy = df/du du/dy df/dv dv/dy How do I get Mathematica to give me df/dx in terms of u, v, and df/du, df/dv?. " % % ( ' !. 1 K h \ _ s Z g b y ?.

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