## 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]=

 f'[x] first derivative of a function of one variable [x] n derivative of a function of one variable [x] derivative of a function of several variables, times with respect to variable i

Output forms for derivatives of unknown functions.

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