If the derivative function is sinx+3, it is a periodic function. Its original function-COSX+3x is not a periodic function.

Let f(x) be a function defined on the number set m. If there is a non-zero constant t whose property is: f(x+T)=f(x), it is said that f(x) is a periodic function on the number set m, and the constant t is called a period of f(x). If there is a minimum in all positive periods, it is called the minimum positive period of the function f(x).

Derivative, also called derivative function value. Also known as WeChat quotient, it is an important basic concept in calculus. When the independent variable x of the function y=f(x) 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 df(x0)/dx.

Extended data:

Determination of periodic function

1, if f(x) is a periodic function with T* as the minimum positive period on set m, then K f(x)+C(K≠0) and 1/ f(x) are set m and set {X/ f(x) ≠0, x respectively.

2. if f(x) is a periodic function with T* as the minimum positive period on set m, then f(ax+n) is a periodic function with T*/ a as the minimum positive period on set {x|ax+b∈M}, where a and b are constants.

3. Let f(u) be a function defined on the set m, and u=g(x) be a periodic function on the set M 1. When X∈M 1, g(x)∈M, the composite function f(g(x)) is M65438+.

4. Let f 1(x) and f2(x) both be periodic functions on the set m, and T 1 and T2 are their periods respectively. If T 1/T2∈Q, their sum, difference and product are also periodic functions on m, and the common multiple of T 1 and T2 is their period.

Baidu Encyclopedia-Periodic Function

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