Question

已知函数y=x³lnx,求y" 麻烦大神弄清楚点万分感谢

Answer 1

y=x^3lnx
y'=(x^3lnx)'
=(x^3)'lnx+x^3(lnx)'
=3x^2lnx+x^3*1/x
=3x^2lnx+x^2
=x^2(3lnx+1)

y''=[x^2(3lnx+1)]'
=(x^2)'(3lnx+1)+x^2(3lnx+1)'
=2x(3lnx+1)+x^2*3*1/x
=6xlnx+2x+3x
=6xlnx+5x