为自己加油

用对数求导法求下列函数的导数：
(1)y=√1-x²√1+2x²
(2)y=(sinx)^cosx
(3)y=(lnx)^lnx
(4)y=e^x/x^e
(5)y=√(x+1)(x+2)/(x+3)(x+4)

(1)由lny=1/2[ln(1一x²)+ln(1+2x²)]， 对y求导，(1/y)y'=1/2[(-2x/1-x²)+(4x/1+2x²)]， 整理得y'=√(1-x²)(1+2x²)•[x(1-4x²)/(1-x²)(1+2x²)]=x(1-4x²)/√(1-x²)(1+2x²) (2)y'=-(sinx)^1+cosxln(sinx)+cos²x(sinx)^-1+cosx =(sinx)^cosx[cos²xcscx一sinxln(sinx)] (3)y'=1/x(lnx)^lnx(1+lnlnx) (4)y'=e^x(x-e)/x^e+1 (5)y'=1/2√[(x+1)(x+2)/(x+3)(x+4)][1/(x+1)+1/(x+2)-1/(x+3)-1/(x+4)]