设shX=[e^x-(1/e)^x]/2,chx=[e^x+(1/e)^x]/2,证明(shx)‘=chx,(chx)’=shx

问题描述:

设shX=[e^x-(1/e)^x]/2,chx=[e^x+(1/e)^x]/2,证明(shx)‘=chx,(chx)’=shx

(shX) '=[e^x-(1/e)^x·(-x) ']/2=[e^x+(1/e)^x]/2=chX
(chX) '=[e^x+(1/e)^x·(-x) ']/2=[e^x-(1/e)^x]/2=shX
证毕