(y: original function; Y': derivative function)

1, y=c, y'=0(c is a constant).

2, y = x μ, y' = μ x (μ- 1) (μ is constant, μ≠0).

3、y=a^x,y'=a^x lna； y=e^x,y'=e^x。

4、y=logax，y ' = 1/(xlna)(a & gt； 0 and a ≠1); y=lnx，y'= 1/x .

5、y=sinx，y’= cosx .

6、y=cosx，y'=-sinx .

7、y=tanx,y'=(secx)^2= 1/(cosx)^2。

8、y=cotx,y'=-(cscx)^2=- 1/(sinx)^2。

9、y=arcsinx,y'= 1/√( 1-x^2)。

10、y=arccosx,y'=- 1/√( 1-x^2)。

1 1、y=arctanx,y'= 1/( 1+x^2)。

12、y=arccotx,y'=- 1/( 1+x^2)。

13、y=shx，y’= CHX .

14、y=chx，y'=sh x .

15、y=thx,y'= 1/(chx)^2。

16、y=arshx,y'= 1/√( 1+x^2)。

Second, what are the basic elementary functions?

(1) constant function y = c( c is a 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.