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.