The Gradient

In[140]:=

  grad2[g][x,y]

Out[140]=

    (1,0)         (0,1)
  {g     [x, y], g     [x, y]}

Note about notation: The first of the above output means the partial derivative of g with respect to x, the second means the partial derivative of g with respect to y.

In[141]:=

  g[x_,y_]:=Exp[- y]Sin[x]

In[142]:=

  grad2[g][x,y]

Out[142]=

   Cos[x]    Sin[x]
  {------, -(------)}
      y         y
     E         E

In[143]:=

  grad3[h][x,y,z]

Out[143]=

    (1,0,0)            (0,1,0)            (0,0,1)
  {h       [x, y, z], h       [x, y, z], h       [x, y, z]}

In[144]:=

  h[x_,y_,z_]:=x y^2 + y^2 z^3 + z^3 x

In[145]:=

  grad3[h][x,y,z]

Out[145]=

    2    3               3       2      2  2
  {y  + z , 2 x y + 2 y z , 3 x z  + 3 y  z }

Chain Rule

Directional Derivatives

The Gradient Vector and Level Curves

Rate of Change and Gradient