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Total DerivativesAdvanced Topic: The Representation of Derivatives

3.5.3 Derivatives of Unknown Functions

Differentiating a known function gives an explicit result.

In[1]:= D[Log[x]^2, x]

Out[1]=

Differentiating an unknown function f gives a result in terms of f'.

In[2]:= D[f[x]^2, x]

Out[2]=

Mathematica applies the chain rule for differentiation, and leaves the result in terms of f'.

In[3]:= D[x f[x^2], x]

Out[3]=

Differentiating again gives a result in terms of f, f' and f''.

In[4]:= D[%, x]

Out[4]=

When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.

In[5]:= D[g[x^2, y^2], x]

Out[5]=

This represents . Mathematica assumes that the order in which derivatives are taken with respect to different variables is irrelevant.

In[6]:= D[g[x, y], x, x, y]

Out[6]=

You can find the value of the derivative when by replacing x with 0.

In[7]:= % /. x->0

Out[7]=

Output forms for derivatives of unknown functions.

Total DerivativesAdvanced Topic: The Representation of Derivatives