The formula for partial derivative of f with respect to x taking y as a constant is given by. The partial derivative at 0 0 must be computed using the limit definition because f is defined in a piecewise fashion around the origin. The derivative of f is called the partial derivative of f.
A partial derivative of a function of several variables expresses how fast the function changes when one of its variables is changed the others being held constant compare ordinary differential equation.
A function which depends on two variables x and y where x and y are independent to each other then we say that the function f partially depends on x and y. Partial differential equation in mathematics equation relating a function of several variables to its partial derivatives. Recall that given a function of one variable f x f x the derivative f x f x represents the rate of change of the function as x x changes. This is an important interpretation of derivatives and we are not going to want to lose it with functions of more than one variable.