Example

Suppose the temperature at each point of a metal plate is given by T(x,y)=Exp[x]Cos[y] + Exp[y]Cos[x].
In what direction does the temperature increase most rapidly at (0,0)? What is the rate of increase?

In[167]:=

  T[x_,y_]:=Exp[x]*Cos[y] + Exp[y]*Cos[x]

In[168]:=

  grad2[T][x,y]

Out[168]=

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

In[169]:=

  grad2[T][x,y]/.{x->0,y->0}

Out[169]=

  {1, 1}

Answer:

Answer: ...

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