Question

求二阶导数,请写明过程,内详.二阶导数,

Answer 1

积法则

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

后面的导数用链式法则

=e^(-x^2)+x*e^(-x^2)*(-x^2)'

=e^(-x^2)+x*e^(-x^2)*(-2x)

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

y''=(1-2x^2)'e^(-x^2)+(1-2x^2)[e^(-x^2)]'

=(-4x)e^(-x^2)+(1-2x^2)e^(-x^2)*(-2x)

=(4x^3-6x)e^(-x^2)