作业帮1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3 2.求二阶导数（y``）：y=(x^2-2x+5)^101.求极限：lim（x趋向0+）lnx/lnsinx 2.单调区间：y=x-e^x
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![1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3 2.求二阶导数（y``）：y=(x^2-2x+5)^101.求极限：lim（x趋向0+）lnx/lnsinx 2.单调区间：y=x-e^x](/uploads/image/z/1698617-65-7.jpg?t=1.%E5%88%A9%E7%94%A8%E5%AF%B9%E6%95%B0%E6%B1%82%E5%AF%BC%E6%B3%95%E6%B1%82%E5%AF%BC%3Ay%3D%5B%28x-1%29x%28x%2B1%29%28x%2B2%29%2F%28x-2%29%5E2%28x%2B3%29%5D%5E1%2F3+2.%E6%B1%82%E4%BA%8C%E9%98%B6%E5%AF%BC%E6%95%B0%EF%BC%88y%60%60%EF%BC%89%EF%BC%9Ay%3D%28x%5E2-2x%2B5%29%5E101.%E6%B1%82%E6%9E%81%E9%99%90%EF%BC%9Alim%EF%BC%88x%E8%B6%8B%E5%90%910%2B%EF%BC%89lnx%2Flnsinx+2.%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%EF%BC%9Ay%3Dx-e%5Ex)
1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3 2.求二阶导数（y``）：y=(x^2-2x+5)^101.求极限：lim（x趋向0+）lnx/lnsinx 2.单调区间：y=x-e^x
1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3 2.求二阶导数（y``）：y=(x^2-2x+5)^10
1.求极限：lim（x趋向0+）lnx/lnsinx
2.单调区间：y=x-e^x
1.利用对数求导法求导:y=[(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3 2.求二阶导数（y``）：y=(x^2-2x+5)^101.求极限：lim（x趋向0+）lnx/lnsinx 2.单调区间：y=x-e^x
1.lny=1/3[ln(x-1)+lnx+ln(x+1)+ln(x+2)-2ln(x-2)-ln(x+3)]
y'/y=1/3[1/(x-1)+1/x+1/(x+1)+1/(x+2)-2/(x-2)-1/(x+3)]
y'=1/3[1/(x-1)+1/x+1/(x+1)+1/(x+2)-2/(x-2)-1/(x+3)][(x-1)x(x+1)(x+2)/(x-2)^2(x+3)]^1/3
2.y'=10(x^2-2x+5)^9(2x-2)=20(x^2-2x+5)^9(x-1)
y"=20[(x^2-2x+5)^9]'(x-1)+20(x^2-2x+5)^9[(x-1)]'
=20[9(x^2-2x+5)^8(x-1)²]+20(x^2-2x+5)^9
=20(x²-2x+5)^8[9(x-1)²+x²-2x+5]
3.lim（x趋向0+）lnx/lnsinx =lim 1/x /(cosx/sinx)=lim sinx/(xcosx)=lim tanx/x=1
4.y'=1-e^x>=0 e^x