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Directional Derivatives in Mathematica


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.


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