取绝对值对数
1.ln|y|=xln|b/a|+aln|x/b|+bln|a/x|
y'/y=ln|b/a|+ln|a/x|+ln|b/x|=ln|b|-ln|a|+ln|a|-ln|x|+ln|b|-ln|x|=2(ln|b/x|)
y'=2(ln|b/x|)y
2.ln|y|=ln|x|+ln|x-1|+ln|x-2|+...+ln|x-n|
y'/y=1/x+1/(x-1)+1/(x-2)+...+1/(x-n)
y'=[1/x+1/(x-1)+1/(x-2)+...+1/(x-n)]y=[1/x+1/(x-1)+1/(x-2)+...+1/(x-n+1)]y+x(x-1)(x-2)...(x-n+1)
把x=n代入得
y'=n(n-1)(n-2)...1=n!