Expert: Paul Klarreich - 10/10/2010

Question
I know you didn't mention multi variable calculus in your
description but could you please help me on this one.

Could you help me find the gradient vector of 200e^((-9x^2-
9y^2)/4-z^2) in terms of x, y and z? Thanks

Answer
Questioner:   Ntokozo
Country:  Canada
Category:  Advanced Math
Private:  No
 
Subject:  Directional Derivatives
Question:  I know you didn't mention multi variable calculus in your
description but could you please help me on this one.

Could you help me find the gradient vector of 200e^((-9x^2-
9y^2)/4-z^2) in terms of x, y and z? Thanks
 
...........................................
The last I heard, gthe gradient vector is simply:

Delta f = <Df/dx,Df/dy,Df/dz>

You simply differentiate w.r.t. x,y,z, one at a time.

I assume you mean: (skip that 200 thing)
               -9x^2 - 9y^2
f(x,y,z) = exp( ------------ )
                  4 - z^2

               -18x
Df[x] = f * (-----------)
              4 - z^2

               -18y
Df[y] = f * (-----------)
              4 - z^2

             (-9x^2 - 9y^2)(-1)(-2z)
Df[z] = f * ( ------------------------ )
                 (4 - z^2)^2

[All routine but messy stuff.]