Question

求下列函数的导数(1)y=x/(1+x²) (2)y=xlnx (3)y=xcosx+根号x (4)y=[3x

Answer 1

(1) y'=[x'(1+x²)-x(1+x²)']/(1+x²)²=(1+x²-2x²)/(1+x²)²=(1-x²)/(1+x²)²

(2) y'=x'lnx+x(lnx)'=1+lnx

(3) y'=x'cosx+x(cosx)'-1/(2√x)=cosx-xsinx-√x/(2x)

(4) y=(3x²+5√x-x√x-9)/√x=3x√x+5-x-(9/√x)=3x^(3/2)+5-x-9x^(-1/2)

y'=3*(3/2)x^(1/2)+0-1-9*(-1/2)x^(-3/2)

=(9√x)/2-1+9/(2x√x)

=(9x²-2x√x+9)/(2x√x)

=(9x²√x-2x²+9√x)/(2x²)