Question

请教求二阶导数

如题：

Answer 1

已经过MATLAB验证，答案保证正确无误。
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y=x*e^(x^2)

y'=【x*e^(x^2)】'
=【x】'*e^(x^2)+x*【e^(x^2)】'…………【公式：y=uv,y'=u'v+uv'】
=e^(x^2)+x*e^(x^2)*【x^2】'
=e^(x^2)+x*e^(x^2)*(2x)
=(2x^2+1)*e^(x^2)

y''=【y'】'
=【(2x^2+1)*e^(x^2)】'
=【e^(x^2)+(2x^2)*e^(x^2)】'
=【e^(x^2)】'+【(2x^2)*e^(x^2)】'
=e^(x^2)*【x^2】'+【(2x^2)】'*e^(x^2)+(2x^2)*【e^(x^2)】'
=(2x)*e^(x^2)+4x*e^(x^2)+(2x^2)*e^(x^2)*【(x^2)】'
=(2x)*e^(x^2)+4x*e^(x^2)+(2x^2)*e^(x^2)*(2x)
=e^(x^2)*(2x+4x+4x^3)
=(6x+4x^3)*e^(x^2)

Answer 2

y'=e^(x²)[1+2x²]

y"=2xe^(x²)[1+2x²]+4xe^(x²).
=4xe^(x²)[1+x²]

Answer 3

求两次导数就可以了
f'=e^(x^2)+2x^2*e^(x^2)
f''=(6x+4x^3)e^(x^2)

Answer 4