高等数学_例题解-16

例16证明双曲函数的导数公式: (Sh x)'=ch x, (ch x )'=sh x,(th x) chix iE(sh x)=d(ex-e-x=H(exte-x)=ch x (ch x)=(e te =(e-e-x)=sh x (th y shy(shx)-chx-shx(chx)_ch2x-sh'x chx ch-x ch-x chix 小: e 上页 结 下页

上页 结束 下页 证 x e e e e x x x x x ( ) ch 2 1 ( ) 2 1 (sh ) = −  = + = − − 证  例16 证明双曲函数的导数公式 x e e e e x x x x x ( ) sh 2 1 ( ) 2 1 (ch ) = +  = − = − −  证 x e e e e x x x x x ( ) ch 2 1 ( ) 2 1 (sh ) = −  = + = − − 证 x e e e e x  x x x x ( ) ch 2 1 ( ) 2 1 (sh ) = −  = + = − − 证 x e e e e x  x x x x ( ) ch 2 1 ( ) 2 1 (sh ) = −  = + = − −  x e e e e x x x x x ( ) sh 2 1 ( ) 2 1 (ch ) = +  = − = − − x e e e e x  x x x x ( ) sh 2 1 ( ) 2 1 (ch ) = +  = − = − − x e e e e x  x x x x ( ) sh 2 1 ( ) 2 1 (ch ) = +  = − = − −  (sh x) =ch x (ch x) =sh x x x 2 ch 1 (th ) =  提示 (e −x )=e −x (−x)=−e −x  x x x x x x x x x x x 2 2 2 2 ch ch sh ch (sh ) ch sh (ch ) ) ch sh (th ) ( − =  −    =  = x 2 ch 1 =  x x x x x x x x x x x 2 2 2 2 ch ch sh ch (sh ) ch sh (ch ) ) ch sh (th ) ( − =  −    =  = x 2 ch 1 =  x x x x x x x x x x x 2 2 2 2 ch ch sh ch (sh ) ch sh (ch ) ) ch sh (th ) ( − =  −    =  = x 2 ch 1 =  x x x x x x x x x x x 2 2 2 2 ch ch sh ch (sh ) ch sh (ch ) ) ch sh (th ) ( − =  −    =  = x 2 ch 1 =  结束