①

C'=0(C is a constant function)

②

(x^n)'=

nx^(n- 1)

(n∈Q *)； Remember the derivative of1/x.

.

③

' sinx '

=

cosx

' cosx '

=

-

Sinks

(tanx)'= 1/(cosx)^2=(secx)^2= 1+(tanx)^2

-(cotx)'= 1/(sinx)^2=(cscx)^2= 1+(cotx)^2

(secx)'=tanx secx

(cscx)'=-cotx cscx

(arcsinx)'= 1/( 1-x^2)^ 1/2

(arccosx)'=- 1/( 1-x^2)^ 1/2

(arctanx)'= 1/( 1+x^2)

(arccotx)'=- 1/( 1+x^2)

(arcsecx)'= 1/(|x|(x^2- 1)^ 1/2)

(arccscx)'=- 1/(|x|(x^2- 1)^ 1/2)

④(sinhx)'=coshx

(coshx)'=sinhx

(tanhx)'= 1/(coshx)^2=(sechx)^2

(coth)'=- 1/(sinhx)^2=-(cschx)^2

(sechx)'=-tanhx sechx

(cschx)'=-cothx cschx

(arsinhx)'= 1/(x^2+ 1)^ 1/2

(arcoshx)'= 1/(x^2- 1)^ 1/2

(artanhx)'= 1/(x^2- 1)

(| x | & lt 1)

(arcothx)'= 1/(x^2- 1)

(| x | & gt 1)

(arsechx)'= 1/(x( 1-x^2)^ 1/2)

(arcschx)'= 1/(x( 1+x^2)^ 1/2)

⑤

(e^x)'

=

e^x

(a^x)'

=

(a^x)lna

(ln is the natural logarithm)

' Inx '

=

1/x(ln is the natural logarithm)

' logax '

=x^(- 1)

/lna(a & gt； 0 and a is not equal to 1)

(x^ 1/2)'=[2(x^ 1/2)]^(- 1)

( 1/x)'=-x^(-2)

I don't remember the fourth category, which is the content of the university.

I hope the answer will help you!