Derivatives of Unknown Functions
Differentiating a known function gives an explicit result.
| Out[1]= |  |
|
Differentiating an unknown function f gives a result in terms of f'.
| Out[2]= |  |
|
Mathematica applies the chain rule for differentiation, and leaves the result in terms of f'.
| Out[3]= |  |
|
Differentiating again gives a result in terms of f, f' and f''.
| Out[4]= |  |
|
When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.
| Out[5]= |  |
|
This represents  . Mathematica assumes that the order in which derivatives are taken with respect to different variables is irrelevant.
| Out[6]= |  |
|
You can find the value of the derivative when x=0 by replacing x with 0.
| Out[7]= |  |
|
| f '[x] | first derivative of a function of one variable |
| f(n)[x] | nth derivative of a function of one variable |
| f (n1, n2, ... )[x] | derivative of a function of several variables, ni times with respect to variable i |
Output forms for derivatives of unknown functions.
