A function of two variables is said to be homogeneous of degree n if whenever . Show that such a function satisfies the equation
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Originally Posted by vuze88 A function of two variables is said to be homogeneous of degree n if whenever . Show that such a function satisfies the equation Derive both sides of wrt and then evaluate the result at . Tonio
Originally Posted by tonio Derive both sides of wrt and then evaluate the result at . Tonio Sorry i still dont fully understand. Can you explain this in more detail. Also im not sure whether the f on the RHS means f(x,y) or f(tx,ty)
Originally Posted by vuze88 Sorry i still dont fully understand. Can you explain this in more detail. Also im not sure whether the f on the RHS means f(x,y) or f(tx,ty) It is exactly as I wrote it: derivate the left side wrt t, derivate the right side wrt t, they're equal, of course, and now put t=1 . Tonio
lol yeah but how to i differentiate with respect to t when the function is in terms of tx and ty
Use the chain rule, of course!
Originally Posted by HallsofIvy Use the chain rule, of course! this is what Euler's theorem on partial derivatives says.
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