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In mathematics, sometimes the function depends on two or more than two variables. In this case, the derivative convert into the partial derivative since the function depends on several variables. Partial derivatives are used in vector calculus and differential geometry.
Definition of Partial Derivative
If we have a function f(x,y) i.e. a function which is depends on two variable x and y, where x and y are independent to each other. Then we say that the function f is partially depends on x and y. At this time if we calculate the derivative of f, then that derivative is called the partial derivative of f. If we differentiate f with respect to x, then taking y as a constant and if we differentiate f with respect to y, then taking x as a constant.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to
one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
For example. suppose f is a function in x and y then it will be denoted by f(x,y). So, partial derivative of f with respect to x will be $\frac<\partial f><\partial x>$ keeping y terms as constant. Note that, it is not dx, instead it is $\partial x$.
Partial Derivative Symbol
The partial derivative of a function f with respect to the variable x is variously denoted by $f'_x$, $f_x$, $\partial_x f$ or $\frac<\partial f><\partial x>$
Here, $\partial$ is the symbol of partial derivative.
Partial Derivative of In
To find the partial derivative of function express in to form of "In", we follow the same procedure as finding the derivative of the function. But, this time when we calculate the partial derivative of the function with respect to one independent variable taking other as constant and follow the same thing with others.
Partial Derivative Examples
Given below are some of the examples on Partial Derivatives.Source: math.tutorvista.com