Y=c(c is a constant) y' = 0；; y=x^n,y'=nx^(n- 1)； y=a^x,y'=a^xlna； y=e^x,y'=e^x； y=logax，y ' = logae/x； y=lnx，y ' = 1/x； y=sinx，y ' = cosxy=cosx，y ' =-sinx； y = tanx y'= 1/cos^2x； y=cotx,y'=- 1/sin^2x。

The derivation methods of conventional tests are as follows:

1. Derive according to the definition of derivative: Derive according to the definition of derivative. Generally, the test is to find the derivative of a point according to the definition of derivative. You need to fully understand what the definition of derivative is about and master the following definition of derivative.

2, the basic formula of the derivative to find the derivative: the basic formula of the derivative * * * has 18, and everything else you see is changed from this 18, and the essence is the same.

3. Four algorithms for derivative: Four algorithms are addition, subtraction, multiplication and division.

4. The law of derivative of inverse function: the derivative of Y to X is the reciprocal of the derivative of X to Y.. It is suitable for exponential functions or functions composed of several elementary functions through multiplication, division, square, square and other operations. Methods: First, both sides of the equation are logarithmic at the same time, and then the derivative is obtained by implicit function derivation.

Expand knowledge:

Derivative is also called derivative function value, also called WeChat service. For the derivative function f(x), xf'(x) is also a function, which is called the derivative function of f(x). The process of finding the derivative of a known function at a certain point or its derivative function is called derivative. Derivative is essentially a process of finding the limit, and the four algorithms of derivative also come from the four algorithms of limit.

Derivative is an important basic concept in calculus and a local property of function. Complex variable function is naturally a problem to be studied on the complex plane. At this time, operations such as derivation in mathematical analysis will naturally be introduced into the complex plane, which leads to the definition of analytic function. Then it is the key to study the properties of analytic functions.

If the derivative of a function exists at a certain point, it is said to be differentiable at that point. The existence of that first derivative at x0 doe not mean that the original function is continuous in a small enough area of x0. The counterexample is: d (x) * x 2, where d is Dirichlet function. It is easy to see that the derivative of this function exists at 0, but it is discontinuous in any small enough region of 0.