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3.5.1 Differentiation


Partial differentiation operations.




  • This gives


    .
  • In[1]:= D[x^n, x]

    Out[1]=

  • This gives the third derivative.
  • In[2]:= D[x^n, {x, 3}]

    Out[2]=

  • You can differentiate with respect to any expression that does not involve explicit mathematical operations.
  • In[3]:= D[ x[1]^2 + x[2]^2, x[1] ]

    Out[3]=

  • D does partial differentiation. It assumes here that y is independent of x.
  • In[4]:= D[x^2 + y^2, x]

    Out[4]=







  • If does in fact depend on , you can use the explicit functional form y[x]. Section 3.5.4 describes how objects like y'[x]


    work.
  • In[5]:= D[x^2 + y[x]^2, x]

    Out[5]=










  • Instead of giving an explicit function y[x], you can tell D that yimplicitly depends on x. D[y,x,NonConstants->{y}] then represents , with implicitly depending on


    .
  • In[6]:= D[x^2 + y^2, x, NonConstants -> {y}]

    Out[6]=