This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Wolfram Research, Inc.

ContentsTotal Derivatives

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 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]

Out[5]=

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}]

Out[6]=

ContentsTotal Derivatives