Definition
Partially Differentiable Function
Let
an open set, a function and . Then,
is called partially differentiable with respect to at , if the limit exists, and partially differentiable with respect to
, if the limit exists. The two limit are called the partial derivatives of
with respect to and , respectively. If both partial derivative exist,
is called partially differentiable. If both partial derivatives exist and both are continuous, then is called continuously partially differentiable function.