求下列函数的二阶导数 2 6题
1个回答

(1) y'=3/5x^(-2/5)

y"=3/5(-2/5)x^(-7/5)

-6/25x^(-7/5)

(2) y'=-2xe^(-x^2)

y"=-2[e^(-x^2)+x(-2x)e^(-x^2)]

=-2e^(-x^2)(1-2x^2)

(3) y'=acosax-bsinbx

y"=-a^2sinax-b^2cosbx

(4) y'=e^xsinx+e^xcosx

=e^x(sinx+cosx)

y"=e^x(sinx+cosx)+e^x(cosx-sinx)

=2cosxe^x

(5) y'=2/(2x)

=1/x

y"=-1/x^2

(6) y'=ln(x+2)+x/(x+2)

y"=1/(x+2)+[(x+2)-x]/(x+2)^2

=(x+2)/(x+2)^2+2/(x+2)^2

=(x+2+2)/(x+2)^2

=(x+4)/(x+2)^2