求下列函数的导数1）y=x^2-2lnx2）y=1/根号下x根号x3）y=1-x^2/根号x4）y=x^5/5+5/x^5+ln55）y=x^10+10^x+10^106）y=x(x+1)(x+2)

Question

求下列函数的导数
1）y=x^2-2lnx
2）y=1/根号下x根号x
3）y=1-x^2/根号x
4）y=x^5/5 + 5/x^5 +ln5
5）y=x^10+10^x+10^10
6）y=x(x+1)(x+2)

Answer 1

1）y=x^2-2lnx
y′=2x-2/x
2）y=1/√(x√x)=x^(-3/4)
y′=(-3/4)x^(-3/4-1)=(-3/4)x^(-7/4)
3）y=(1-x^2)/√x
y′=[-2x*√x-(1-x^2)*1/2√x]/x
=-2√x-(1-x^2)/2x√x
4）y=x^5/5 + 5/x^5 +ln5
y′=x^4+5*(-5)x^(-5-1)=x^4-25/x^6
5）y=x^10+10^x+10^10
y′=10x^9+10^x*ln10
6）y=x(x+1)(x+2)=x^3+3x^2+2x
y′=3x^2+6x+2