A partial derivative is a mathematical concept used in multivariable calculus to calculate how a function changes when only one of its variables is altered while keeping the other variables constant.
Partial derivatives are important because they allow us to analyze how a function changes in response to different variables, and are essential in many fields of science and engineering, such as physics and economics.
To calculate a partial derivative, one must take the derivative of the function with respect to the specific variable of interest, treating all other variables as constants.
A partial derivative only considers changes in one variable, while a total derivative takes into account changes in all variables simultaneously. In other words, a total derivative is the sum of all partial derivatives of a function.
Partial derivatives are used in many areas of science and engineering, such as optimization problems, thermodynamics, and risk management in finance. They are also used in computer science for image and signal processing.