: is the classical writing of the Greek letter δ, which is only used as the symbol of partial derivative in mathematics. When expressing partial derivatives, letter names are generally not pronounced, but most people in China pronounce them as deviations. For example, the partial derivative of z to x is pronounced as part z and part X.
The partial derivative of a multivariable function is its derivative of one variable, while keeping the total derivative of other variables unchanged, in which all variables are allowed to change. Partial derivatives are very useful in vector analysis and differential geometry.
Partial derivative definition
In a unary function, the derivative is the rate of change of the function. It is much more complicated to study the change rate of binary function because there is one more independent variable. On the xOy plane, when the moving point changes from P(x0, y0) to different directions, the change speed of the function f(x, y) is generally different, so it is necessary to study the change rate of f(x, y) in different directions at (x0, y0).
Here we only study the change rate of the function f(x, y) when it changes in two special directions parallel to the X axis and parallel to the Y axis. The partial derivative reflects the rate of change of the function along the positive direction of the coordinate axis. The partial derivative of a multivariable function is its derivative of one variable, while keeping other variables unchanged. Partial derivatives are very useful in vector analysis and differential geometry.