Question

1.y=[(b/a)的x次方]乘以[(x/b)的a次方]乘以[(a/x)的b次方] 2.y=(x-1)(x-2)^2..

Answer 1

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!