例2y= SInn·six J= n. cosnX·sin"x+ SInn·n·Si(n-1) x. cost =n sin" x(cos nx.sin x+sin nx. cos x) =n sin"xsin(n+1)x
例2 y nx x n = sin sin y n nx x nx n x x n n cos sin sin sin cos ( 1) = + − sin (cos sin sin cos ) 1 n x nx x nx x n = + − n x n x n sin sin( 1) 1 = + −
例3求函数y=fp"(sinx")的导数 解y'=nf"qp"(sinx")·∫'φ"(sinx") nop(sinx")φp'sinx")·cosx"·nx =n3·x"cosx"·f∫"Iq"(sinx") φ"(sinx")·∫1φ"(sinx")φp(sinx")
例 3 求函数 [ (sin )]的导数. n n n y = f x 解 [ (sin )] [ (sin )] n 1 n n n n y = nf x f x − (sin ) (sin ) n 1 n n n x x − 1 cos − n n x nx (sin ) [ (sin )] (sin ). cos [ (sin )] 13 1 1 n n n n n n n n n n x f x x n x x f x = − − −