例、设y dy In cos(e ),求 d 解: dy dx (sin(e ) tan(e cos(e 例、设y=ln(x+yx2+1),求y 解:y ( 2x x+ 2√x2+1 √x2+ shx 记 arsh x=ln(x+√x2+1),则 的反函数 (反双曲正弦) arsh x 2 ②0∞例、设 求 解: cos( ) 1 x e = ( sin( )) x  − e x  e tan( ) x x = −e e 例、设 解: 1 1 2 x + x + ( 1+ 2 1 1 2 x +  2x ) 1 1 2 + = x 记 arsh ln( 1) , 2 x = x + x + 则 (arsh x) = 1 1 2 x + (反双曲正弦) 2 sh x x e e x − − = 的反函数