Directional Derivatives in Mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg5694] Directional Derivatives in Mathematica*From*: "Jose M. de Aguiar" <jmaguiar at leland.Stanford.EDU>*Date*: Sat, 11 Jan 1997 14:28:59 -0500*Organization*: Stanford University*Sender*: owner-wri-mathgroup at wolfram.com

Please, I am trying to have make mathematica to produce derivatives in terms of directions given by vectors taken along a curve. Let me explain: Say I have a function w(x,y)=(r^2)*Log[r], being r the distance between a point P(xP,yP) and a point Q(x,y) on a curve. Say {t,n} are vectors along the tangential and normal direction along the curve. How can I instruct mathematica to give me derivatives of the type: w,t=(r,t)*(Log[r]) + r*(1/r)*r,t=(r,t)*(1+Log[r]) w,tn=(r,tn)*(1+Log[r]) + (r,t)*((1/r)*r,n) ? In other words: I don't want expressions of {r,t and r,n} to be presented in terms of {xP,x,yP,y}. I want to keep working with them, as shown above. Thanks for any help or suggestion on the problem. Jose.