1, y=c(c is a constant) y'=0.
2、y=xAn y'=nx^(n- 1)。
3、y=aAx y'=aAxlna，y=eAxy'=eAx .
4、y=logax y'=logae/x，y=Inx y'= 1/x .
y=sinx y'=cosx .
y=cosx y'=-sinx .
7、y=tanx y'= 1/cos^2x。
8、y=cotx y'=- 1/sin A2x .
9、y = arcsinxy'= 1/v 1-x^2。
10、y = arc cosxy'=- 1/v 1-x^2。
1 1、y = arctanxy'= 1/ 1+x^2。
12、y = arccotx y ' =- 1/ 1+xA2 .
Derivative is an important basic concept in calculus. The limit of the quotient between the increment of the dependent variable and the increment of the independent variable when the increment of the independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable. Derivative is essentially a process of finding the limit, and the four algorithms of derivative come from the four algorithms of limit.
The above formula can be proved by the nature of derivative, which is the slope of the tangent of the function at a certain point, that is, the ratio of the increment of the function value to the increment of the independent variable near that point (the increment of the independent variable approaches zero).
Characteristics of derivative products:
Odd function derivative is not necessarily an even function, for example, let f(x) = x 2, (x0), and f(x) is not defined at the origin, so it is not an even function. But f'(x)=2x(x is not equal to 0) is odd function.
Derivation is a calculation method in mathematical calculation, which is defined as the limit of the quotient between the increment of dependent variable and the increment of independent variable when the increment of independent variable tends to zero. When a function has a derivative, it is said to be derivative or differentiable. The differentiable function must be continuous. Discontinuous functions must be non-differentiable. Derivation is the basis of calculus.
It is also an important pillar of calculus calculation. Some important concepts in physics, geometry, economics and other disciplines can be expressed by derivatives. For example, derivatives can represent the instantaneous speed and acceleration of a moving object, the slope of a curve at a certain point, and the margin and elasticity in economics.