The Gradient

  grad2[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.

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

  grad2[g][x,y]

  grad2[h][x,y]

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

  grad3[h][x,y,z]

Chain Rule

Directional Derivatives

The Gradient Vector is Perpendicular to the Level Curve

Rate of Change and Gradient