1、ⅹ→0，lim(sinⅹ/ⅹ)=1
lim(1-cosⅹ)/ⅹ=0
sin(A B)=sinAcosB cosAsinB
cos(A B)=cosAcosB-sinAsinB
2、y=sinⅹ
y＇=(sin(ⅹ h)-sinⅹ)/h=
(sinⅹcosh cosⅹsinh-sinⅹ)/h=
sinⅹ((cosh-1)/h) cosⅹ(sinh/h)=
cosⅹ
3、y=cosⅹ
y′=(cos(ⅹ h)-cosⅹ)/h=
(cosⅹcosh-sinⅹsinh-cosⅹ)/h=
cosⅹ((cosh-1)/h)-sinⅹ(sinh/h)=
-sinⅹ
4、y=tanⅹy=sinⅹ/cosⅹ
y＇=
(cosⅹcosⅹ-(-sinⅹ)sinⅹ)/cos²ⅹ
=1/cos²ⅹ=sec²ⅹ
5、y=cotⅹ=1/tanⅹ
令μ=tanⅹ，y=1/μ→
y＇=(dy/dμ)(dμ/dⅹ)=
(-1/μ²)(1/cos²ⅹ)=
-(cos²ⅹ/sin²ⅹ)(1/cos²ⅹ)=-csc²ⅹ
6、y=secⅹ=1/cosⅹ，令μ=cosⅹ→y=1/u→
y′=(dy/dμ)(dμ/dⅹ)=
(-1/μ²)(-sinⅹ)=(-1/cos²ⅹ)(-sinⅹ)
==secⅹtanⅹ
7、y=cscⅹ=1/sinⅹ，μ=sinⅹ→
y=1/μ→y＇=(dy/du)(dμ/dⅹ)=
(-1/μ²)(cosⅹ)=(-1/sin²ⅹ)(cosⅹ)=
-cscⅹcotⅹ
