If the real function is defined in the point and on some interval right from this and if the right-hand one-sided limit exists, then this limit is defined to be the right-sided derivative of in .
It’s apparent that if has both the left-sided and the right-sided derivative in the point and these are equal, then is differentiable in and equals to these one-sided derivatives. Also inversely.
Example. The real function is defined for and differentiable for with . The function also has the right derivative in :
Remark. For a function , to have a right-sided derivative at with value , is equivalent to saying that there is an extension of to some open interval containing and satisfying . Similarly for left-sided derivatives.
|Date of creation||2013-03-22 15:39:00|
|Last modified on||2013-03-22 15:39:00|
|Last modified by||pahio (2872)|