1. Definition method: According to the definition of derivative, finding derivative means finding the rate of change of function. Suppose the function f(x) is defined at point X, choose a point x0 to make x0 close to X, and calculate the difference between f(x0) and f(x), which is the approximate change rate of f(x) at point X. By choosing different x0, we can get different approximate change rates, and the average of these change rates is the derivative of f(x) at point X.

2. Formula method: The derivatives of many basic functions have been pre-calculated and can be directly quoted. For example, the derivative of constant is 0, the derivative of power function is exponential multiple of function value, and the derivative of trigonometric function is the derivative of sine, cosine, tangent and other functions.

3. Derivation of compound function: If a function is composed of several basic functions, then its derivative can be calculated by the derivative rule of compound function. Specifically, if both f(u) and u(x) are differentiable, the derivative of the composite function f(u(x)) can be expressed as f'(u(x))u'(x).

4. Derivation of implicit function: In some cases, the form of function is hidden, not explicit. For example, the equation y2=x+3 can be regarded as an implicit function. For such a function, we can get the derivative by taking the derivative of both sides of the equation at the same time.

5. Logarithmic derivation: For some complex function forms, it may be difficult to derive directly. At this time, we can use logarithmic derivative's law to simplify the calculation. Specifically, if f(x) is differentiable and not zero, the derivative of f(x) can be obtained by finding the logarithm of f'(x) and then taking the exponent.

Related knowledge of derivative products

1, derivation is an important concept in calculus, which refers to the differential operation of a function, so as to obtain the derivative of the function. Derivative can reflect the rate of change of function, that is, the degree of change of function value with independent variables.

2. The basic method of derivative is to use derivative formula or rule. Common derivative formulas include addition, subtraction, multiplication, division and derivative rules of power function. These rules can be combined to obtain more complex functions.

3. Derivation is widely used in mathematics, physics, engineering and other fields. For example, in economics, derivatives can be used to analyze the changing trends of variables such as costs and benefits; In physics, derivatives can be used to describe the changing laws of kinematic variables such as speed and acceleration. In engineering, derivatives can be used to study the changes of variables such as temperature, pressure and flow.

4. Besides the basic derivative formula, there are some special derivative methods, such as chain rule, product rule, differential rule and so on. These rules can be used to export certain types of functions, thus making the calculation easier.

5. Derivation can also be extended to partial derivatives and total differentiation of multivariate functions. Partial derivative represents the rate of change of a function to an independent variable, while total differential represents the rate of change of a function to all independent variables. These concepts have important application value in extremum and optimization of multivariate functions.