Partial derivative

In multivariable calculus, the partial derivative of a function is the derivative of one variable when all other variables are held constant. In other words, a partial derivative takes the derivative of certain variables of a function while not differentiating other variable(s). Partial derivatives are often used in multivariable functions. 

For partial derivatives of function f with respect to variable x, the notation 

,  , 

is standard, but other notations are sometimes used.

 Examples 
If we have a function , then there are several partial derivatives of f(x, y) that are all equally valid. For example,

Or, we can do the following:

Related pages
Difference quotient
Partial differential equation

 References 

Category:Calculus