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3.5.1 Differentiation

Partial differentiation operations.

This gives .

In[1]:= D[x^n, x]


This gives the third derivative.

In[2]:= D[x^n, {x, 3}]


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] ]


D does partial differentiation. It assumes here that y is independent of x.

In[4]:= D[x^2 + y^2, x]


If y does in fact depend on x, 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]


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

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


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