higher order derivatives
the so-called derivative function of ; it is denoted by
or simply .
Forming the derivative function of a function is called differentiation, the corresponding verb is differentiate.
If the derivative function is differentiable on , then we have again a new function, the derivative function of the derivative function of , which is denoted by . Then is said to be twice differentiable. Formally,
The function is called the or the second derivative of . Similarly, one can call (1) the of .
Example. The first derivative of is and the second derivative is , since
If also is a differentiable function, its derivative function is denoted by and called the of , and so on.
Generally, can have the derivatives of first, second, third, …, th order, where may be an arbitrarily big positive integer. If is four or greater, the th derivative of is usually denoted by . In , it’s sometimes convenient to think that the th order derivative of is the function itself.
The phrase “ is infinitely differentiable” means that has the derivatives of all .
|Title||higher order derivatives|
|Date of creation||2013-03-22 16:46:30|
|Last modified on||2013-03-22 16:46:30|
|Last modified by||PrimeFan (13766)|
|Defines||order of derivative|