√{(X+1)(X+2)/(X+3)(X+4)}

题目

√{(X+1)(X+2)/(X+3)(X+4)}
即根号里面的分子是(X+1)(X+2),分母是(X+3)(X+4).其导数应该怎么求呢?我
参考答案里面给的是
1/2*√{(X+1)(X+2)/(X+3)(X+4)}*{1/（X+1）+1/(X+2)-1/(X+3)-1/(X+4)}
请问这个是怎样求导的呢?

答案

设y=√{(X+1)(X+2)/(X+3)(X+4)} 则lny=1/2[ln(x+1)+ln(x+2)-ln(x+3)-ln(x+4)]两边求导,注意y是复合函数y'/y=1/2[1/(x+1)+1/(x+2)-1/(x+3)-1/(x+4)]y'=1/2*y*[1/(x+1)+1/(x+2)-1/(x+3)-1/(x+4)]=1/2*√{(X+1)(X+2)/(X...