Re: Implicit Derivatives

*To*: mathgroup at smc.vnet.net*Subject*: [mg26215] Re: [mg26193] Implicit Derivatives*From*: BobHanlon at aol.com*Date*: Sat, 2 Dec 2000 02:10:41 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

eq = (3 x y == x^3 + y^3); Solve[D[eq /. y -> y[x], x], y'[x]] // Simplify {{Derivative[1][y][x] -> (x^2 - y[x])/(x - y[x]^2)}} Solve[Dt[eq, x], Dt[y, x]] // Simplify {{Dt[y, x] -> (x^2 - y)/(x - y^2)}} Solve[Dt[eq], Dt[y]] // Simplify {{Dt[y] -> ((x^2 - y)*Dt[x])/(x - y^2)}} Bob Hanlon In a message dated 11/30/00 10:30:32 PM, tdevries at shop.westworld.ca writes: >I am teaching a high school calculus class and we are using Mathematica >for >part of the course work. In the book CalcLabs with Mathematica they >give >a procedure for finding an Implicit Derivative. Here is an example with >a >familiar equation.... > >eq = (3 x y == x^3 + y^3) > >eqNew = eq /. y -> y[x] > >deqNew = D[eqNew, x] > >soln = Solve[deqNew, y'[x]] > > >I am wondering if there are other ways to get a similar result to this. > >This method makes sense to me but I wondered if there was a more direct >approach? I could not find any information using the Help feature but >perhaps I was just looking in the wrong places? >