And the partial derivative is the contribution of each partial derivative to this function. You only remember one thing, to find the partial derivative is to treat other parameters as constants. For example, the partial differential is as follows: df= 1dx+2dy+3dz. It means that 1, 2 and 3 represent the partial derivatives of x, y, z, y and z respectively. F(x, y, z) is the expected function.
Extended data:
In mathematics, the partial derivative of a multivariable function is its derivative of one variable, while keeping other variables unchanged (compared with the total derivative, all variables in the total derivative are allowed to change). Partial derivatives are very useful in vector analysis and differential geometry.
Partial derivative in x direction
There is a binary function z=f(x, y), and the point (x0, y0) is a point on its domain d, with y fixed at y0 and x at x0? There is an increment △x, and accordingly the function z=f(x, y) also has an increment (called partial increment to x) △z=f(x0+△x, y0)-f(x0, y0).
If the limit of the ratio of △z to △x exists when △x→0, then this limit value is called the partial derivative of the function z=f(x, y) to x at (x0, y0), and it is recorded as f'x(x0, y0) or. The partial derivative of function z=f(x, y) to x at (x0, y0) is actually the derivative of univariate function z=f(x, y0) at x0 after y is fixed at y0 as a constant.
Partial derivative in y direction
Similarly, if x is fixed at x0, let y have an increment △ Y, and if there is a limit, then this limit is called the partial derivative of the function z=(x, y) to y at (x0, y0). Write f'y(x0, y0).
When the function z=f(x, y) exists in the partial derivatives of f 'x (x0, y0) and f'y(x0, y0), we say that f(x, y) is derivable at (x0, y0). If the function f(x, y) is differentiable at every point in the domain d, it is said that the function f(x, y) is differentiable in the domain d.
At this time, every point (x, y) in D domain must have a partial derivative of X (for Y), so a new binary function is determined in D domain, which is called the partial derivative function of f(x, y) for X (for Y). Partial derivative for short.
According to the definition of partial derivative, when a multivariate function takes partial derivative of one independent variable, the other independent variables are regarded as constants. At this time, his derivative method is the same as that of the unary function.
References:
Baidu encyclopedia-partial derivative? Baidu encyclopedia-partial differential equation