When the independent variable x of the function y=fx generates an increment δ x at the point x0, if there is a limit a in the ratio of the increment δ y of the function output value to the increment δ x of the independent variable when δ x tends to 0, then A is the derivative at x0, which is denoted as f'x0 or dfx0/dx.
Derivative algorithm is a function composed of the sum, difference, product and quotient of basic functions, and the derivative function can be derived from the derivative rule of the function. The linearity of derivative is the derivative of linear combination of functions, which is equivalent to taking the derivative of each part first and then taking the linear combination. The derivative function of the product of two functions is the first derivative times two+the first derivative times two.
The methods of derivation include definition method, formula method, implicit function method, logarithm method and compound function method. Definition method uses the definition of derivative to get derivative, formula method uses given formula to get derivative, implicit function method uses implicit function to get derivative, logarithmic method uses logarithm to get derivative, and composite function method uses composite function to get derivative.
Higher mathematics refers to a more complicated part of mathematical objects and methods compared with elementary mathematics and secondary mathematics. Algebra, geometry and simple set theory in middle schools are called secondary mathematics, which is regarded as the transition between elementary mathematics in primary and secondary schools and advanced mathematics in universities.
Curriculum characteristics
Generally speaking, advanced mathematics is a basic subject formed by calculus, algebra, geometry and their intersection after17th century. Compared with elementary mathematics and secondary mathematics, mathematics is more difficult to learn, which belongs to university courses, so it is often called advanced mathematics, and it is often called calculus and science and engineering in teaching materials.
Students majoring in literature and history learn mathematics shallowly, and different majors in literature and history have different depths. It is advanced mathematics that studies variables, but advanced mathematics does not only study variables. As for the courses related to "advanced mathematics", there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study independently).