[Date Index]
[Thread Index]
[Author Index]
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
Prev by Date:
**Re: Plot3D, show and text**
Next by Date:
**Re: release memory**
Previous by thread:
**Re: Partial derivatives for implicit functions**
Next by thread:
**Re: Partial derivatives for implicit functions**
| |