求下列函数的导数：
(1)y=sin(2x+3)；
(2)y=e1/x；
(3)y=ln[x-√(x2-1)]；
(4)y=arctan(x/2)；
(5)y=sin(cos1/x)．
【正确答案】：(1)y'=(2x+3)' cos(2x+3) =2cos(2x+3)． (2)y'=(1/x)'e1/x =-1/x2e1/x (3)y'=(x-√(x2-1))'×1/[x-√(x2-1)] =[1-2x/2√(x2-1)][x+√(2-1)] =[1-x/√(x2-1)][x+√(x2-1)] =-1/√(x2-1) (4)y'= 1/[1+(x/2)2]•(x/2)' =4/4+x2•1/2 (5)y'=cos(cos1/x)•(cos1/x)' =-cos(cos1/x)•sin(1/x)•(1/x)' =1/x2cos(cos1/x)•sin(1/x)．
