RE: Partial derivatives for implicit functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg98333] RE: [mg98303] Partial derivatives for implicit functions*From*: "David Park" <djmpark at comcast.net>*Date*: Mon, 6 Apr 2009 05:02:19 -0400 (EDT)*References*: <6934246.1238929226790.JavaMail.root@n11>

Srikanth, Use implicit differentiation. Copy and evaluate the following in one cell. Print["Find dy/dx for the equation:"] eqn1 = 2 y == x^2 + Sin[y] Print["To calculate dy/dx implicitly write equation with y as a \ function of x."] eqn2 = eqn1 /. y -> y[x] Print["Differentiate with respect to x"] step1 = D[eqn, x] Print["Solve the equation for y'[x]."] step2 = Equal @@ Part[Solve[step1, y'[x]], 1, 1] Print["Change y[x] back to y."] step3 = step2 /. y[x] -> y Print["Get rid of the extra minus signs."] MapAt[Minus, step3, {{2, 1}, {2, 3, 1}}] If you have Presentations you could also get rid of the minus signs with: Needs["Presentations`Master`"] MapAt[MultiplyByOne[-1], step3, 2] which multiplies numerator and denominator by -1. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Srikanth [mailto:skt at xdtech.com] Hi I have a function f(x,y,z)=0. I would like to find dx/dy and dx/dz (where I am using d for partial derivatives, I'm not sure how to get the actual symbol in this edit box), where both would be functions of x, y and z. Unfortunately, I cannot get an explicit solution x=g(y,z). Any ideas on how I'd go about solving this? Thanks Srikanth