# Defining Derivatives

You can define the derivative in the Wolfram Language of a function f of one argument simply by an assignment like f'[x_]=fp[x].

This defines the derivative of to be . In this case, you could have used = instead of :=:
 In:= The rule for f'[x_] is used to evaluate this derivative:
 In:= Out= Differentiating again gives derivatives of :
 In:= Out= This defines a value for the derivative of at the origin:
 In:= Out= The value for g' is used:
 In:= Out= This defines the second derivative of g, with any argument:
 In:= Out= The value defined for the second derivative is used:
 In:= Out= To define derivatives of functions with several arguments, you have to use the general representation of derivatives in the Wolfram Language.

 f'[x_]:=rhs define the first derivative of f Derivative[n][f][x_]:=rhs define the n derivative of f Derivative[m,n,…][g][x_,_,…]:=rhs define derivatives of g with respect to various arguments

Defining derivatives.

This defines the second derivative of g with respect to its second argument:
 In:= This uses the definition just given:
 In:= Out= 