作业帮求导（6题,求详解）谢谢(√这个是根号）1.y=2√x-1/x+4√32.y=(√x+1)(1/√x-1)3.y=(ax+b)/(a+b)4.y=(x+1)(x+2)(x+3)5.y=loga√x6.y=(1-lnx)/(1+lnx)
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/28 14:22:14
求导（6题,求详解）谢谢(√这个是根号）1.y=2√x-1/x+4√32.y=(√x+1)(1/√x-1)3.y=(ax+b)/(a+b)4.y=(x+1)(x+2)(x+3)5.y=loga√x6.y=(1-lnx)/(1+lnx)
求导（6题,求详解）
谢谢(√这个是根号）
1.y=2√x-1/x+4√3
2.y=(√x+1)(1/√x-1)
3.y=(ax+b)/(a+b)
4.y=(x+1)(x+2)(x+3)
5.y=loga√x
6.y=(1-lnx)/(1+lnx)
求导（6题,求详解）谢谢(√这个是根号）1.y=2√x-1/x+4√32.y=(√x+1)(1/√x-1)3.y=(ax+b)/(a+b)4.y=(x+1)(x+2)(x+3)5.y=loga√x6.y=(1-lnx)/(1+lnx)
1.
y=2√x-1/x+4√3=2x^(½) - x^(-1) + 4√3
dy/dx=2×½x^(-½) + x^(-2) + 0
= 1/x^(½) + 1/x²
2.
y=(√x+1)(1/√x-1)
=1 - √x + 1/√x -1
=-√x + 1/√x
=-x^(½) + x^(-½)
dy/dx=-(½)x^(-½)-(½)x^(-3/2)
=-(1/2√x)(1+1/x)
3.
y=(ax+b)/(a+b)=ax/(a+b) + b/(a+b)
dy/dx=a/(a+b) + 0 =a/(a+b)
4.
y=(x+1)(x+2)(x+3)
dy/dx=(1+0)(x+2)(x+3)+(x+1)(1+0)(x+3)+(x+1)(x+2)(1+0)
=(x+2)(x+3)+(x+1)(x+3)+(x+1)(x+2)
=x²+5x+6+x²+4x+3+x²+3x+2
=3x²+12x+11
or
y=(x+1)(x+2)(x+3)=x³+6x²+11x+6
dy/dx=3x²+12x+11
5.
y=loga√x=½ logax=½(lnx)/lna
dy/dx=(½)(1/x)lna=(ln√x)/x
6.
y=(1-lnx)/(1+lnx) =-(1+lnx-2)/(1+lnx)=-1+2/(1+lnx)
dy/dx=0-[2/(1+lnx)²]×(1/x)
=-2/[x(1+lnx)²]