例5在下列等式左端的括号中填入适当的函数使 等式成立 (1)d( )=cos otdr; (2)(sinx)=( d(x) R (1). d(sin or)=@o cos otdr, cos tdt=d(sin at)=d(sin ot) ∴d(sint+C)= cos tdt. d(sin x) 2x cos x dx 4x√xc0sx, 2√x ∴d(sinx2)=(4x√ x cos r2)d(√x)14 例5 解 在下列等式左端的括号中填入适当的函数,使 等式成立. (1) ( ) cos ; (2) (sin ) ( ) ( ). 2 d = tdt d x = d x (1)d(sint) = costdt, (sin ) 1 cos tdt d t    = sin ) cos . 1 d( t + C = tdt   sin ); 1 d( t  = dx x x x dx d x d x 2 1 2 cos ( ) (sin ) (2) 2 2  = 4 cos , 2 = x x x (sin ) (4 cos ) ( ). 2 2 d x = x x x d x