2. Find the first derivative of x on both sides of the original equation. This equation must contain both the first derivative and the second derivative of X. Finally, the equation containing only the second derivative can be obtained by substituting the first derivative obtained in 1 into it.
(1) In mathematics, the partial derivative of a multivariable function is the derivative of a variable while keeping other variables unchanged (compared with the full derivative, the full derivative allows all variables to change). Partial derivatives are very useful in vector analysis and differential geometry.
(2) Geometric significance
Represents the tangent slope of a point on a fixed surface.
The partial derivative f'x(x0, y0) represents the tangent slope of a point on a fixed surface to the X axis; The partial derivative f'y(x0, y0) represents the tangent slope of a point on a fixed surface with respect to the y axis.
Higher-order partial derivatives: If the partial derivatives f'x(x, y) and f'y(x, y) of the binary function z=f(x, y) are still derivable, then the partial derivatives of these two partial derivatives are called the second-order partial derivatives of z=f(x, y). Binary function has four second-order partial derivatives: f"xx, f"xy, f"yx, f"yy.
note:
The difference between f "xy" and f "yx" is that the former takes the partial derivative of x first, and then takes the partial derivative of y from the obtained partial derivative function; The latter takes the partial derivative of y first, and then the partial derivative of x. When f "xy" and f "yx" are continuous, the result of derivative is independent of order.
References:
Baidu encyclopedia: partial derivative