设y=√(x+1)(x2+1)3/(x+2)2ex，求y'．

设y=√(x+1)(x²+1)³/(x+2)²e^x，求y'．
【正确答案】：对已知函数取对数得 lny=(1/2)ln(x+1)+3ln(x²+1)-2ln(x+2)-x， 两边对x求导得 y'/y=1/2(x+1)+6x(x²+1)-2/(x+2)-1， 所以 y'=√(x+1)(x²+1)³/(x+2)²e^x[1/2(x+1)+6x(x²+1)-2/(x+2)-1]