Derivatives of Unknown Functions
Differentiating a known function gives an explicit result.
Differentiating an unknown function f
gives a result in terms of f'
applies the chain rule for differentiation, and leaves the result in terms of f'
Differentiating again gives a result in terms of f
When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.
assumes that the order in which derivatives are taken with respect to different variables is irrelevant.
You can find the value of the derivative when x=0
by replacing x
|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.