1,
y=(x²-x)/(x+√x)
y'=[(2x-1)(x+√x)-(x²-x)(1+1/(2√x))]/(x+√x)²
=[2x²+2x√x-x-√x-x²-1/2x^(3/2)+x+1/2√x]/(x+√x)²
=[x²+3/2x√x-1/2√x]/(x+√x)²
2,y=cos2x/(sinx+cosx)
=(cos²x-sin²x)/(cosx+sinx)
=(cosx+sinx)(cosx-sinx)/(cosx+sinx)
=cosx-sinx
y'=-sinx-cosx
3
,y=(x-2√x)四次方
y'=4(x-2√x)³(1-1/√x)
4
.y=xe^(-2x)
y'=e^(-2x)+xe^(-2x)*(-2)
=e^(-2x)(1-2x)