Partial derivative online calculator
Partial derivative concept is only valid to the multivariable functions. Examine two variable function
z=f(
x,y).
Partial derivative by variables x and y are denoted as
and
correspondingly. The partial derivatives
and
by themselfs are also the two variable functions:
and
, so their partial derivatives can also be found:
Derivatives
and
are the second order partial derivatives of the function z by the variables x and y correspondingly.
Derivatives
and
are called mixed derivatives of the function z by the variables x, y and y, x
correspondingly. If the function z and their mixed derivatives
and
are defined at some neighborhood of a point
M(x0,y0)
and continuous at that point, then the following equality is valid:
Similary, one can introduce the higher order derivatives, for instance
means that we should differentiate the function
z two times by the variable x
and three times by the variable y, so:
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Sometimes, in order to denote partial derivatives of some function
z=f(x,y)
notations
fx'(x,y) and
fy'(x,y) are
used. Subscript index is used to indicate the differentiation variable. Using this approach one can denote mixed derivatives:
fxy''(x,y) and
fyx''(x,y)
and also the second and higher order derivatives:
fxx''(x,y) and
fxxy'''(x,y)
accordingly. Following notations are equivalent:
,
however, usually digit 1 is absent. To denote partial derivatives in our online calculator, we use symbols:
.
Example of step by step solution can be found
here.
Expression input type: