Implicit Derivatives
- To: mathgroup at smc.vnet.net
- Subject: [mg5733] Implicit Derivatives
- From: jmaguiar at leland.stanford.edu
- Date: Sat, 11 Jan 1997 14:29:19 -0500
- Organization: Stanford University
- Sender: owner-wri-mathgroup at wolfram.com
Please,
I have the following problem:
Let w(xP,yP,x,y)=(r^2)Log[r] being r =Sqrt[(x-xP)^2 + (y-yP)^2] the
distance
between point P(xP,yP) and Q(x,y). Let {t,n} be the tangent and normal
vectors
to a boundary curve at Q.
How can I instruct mathematica to produce the derivatives of function w
in terms of
{r,t ; r,n; r,tn} ? In other words: how can I obtain the following
expresions:
w,t =2*r*(r,t)*Log[r] + r*(1/r)*(r,t)=r*(1+Log[r])*(r,t)
w,nt=(r,n)*(1+Log[r])*(r,t) + r*(1/r)*(r,n)*(r,t) +
r*(1+Log[r])*(r,nt) ?
Thanks for any suggestion.