16 Derivation formula of basic elementary function 1.y=c y'=0.
2.y=α^μ y'=μα^(μ- 1)
3.y=a^x y'=a^x lna
y=e^x y'=e^x
4.y=loga，x y'=loga，e/x
y=lnx y'= 1/x
5.y=sinx y'=cosx
6.y=cosx y'=-sinx
7.y = Tanks Y' = (secx) 2 =1/(cosx) 2
8.y = cotx y'=-(cscx)^2=- 1/(sinx)^2
9.y = arc sinx y'= 1/√( 1-x^2)
10 . y = arc cosx y'=- 1/√( 1-x^2)
1 1 . y = arc tanx y'= 1/( 1+x^2)
12 . y = arc cotx y'=- 1/( 1+x^2)
13.y=sh x y'=ch x
14.y=ch x y'=sh x
15 . y = thx y'= 1/(chx)^2
16 . y = ar y'= 1/√( 1+x^2)
17 . y = ar CHX y'= 1/√(x^2- 1
18 . y = y'= 1/( 1-x^2)
What does the basic elementary function include? (1) Constant function y = c( c is constant).
(2) power function y = x^a( a is a constant)
(3) exponential function y = a x(a >；; 0，a≠ 1)
(4) logarithmic function y = log (a) x (a >; 0, a≠ 1, real number x>0)
(5) trigonometric functions and inverse trigonometric functions (such as sine function: y =sinx sine function: y = sine x, etc.). )
The basic elementary function, the so-called elementary function, is the function that the basic elementary function is composed of four operations and several times. Elementary function is a function composed of basic elementary functions through finite rational operations and compounding, which can be expressed by a formula. Basic elementary functions and elementary functions are continuous functions within their defined intervals. Functions that are not elementary functions are called non-elementary functions, such as Dirichlet function and Riemann function.