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MathGroup Archive 1997

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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.


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