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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]= 
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