请帮我求二阶偏导数~1.已知Z=x^3siny+y^3sin,求(ə^2z)/( əxəy

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/10/04 06:27:15

请帮我求二阶偏导数~
1.已知Z=x^3siny+y^3sin,求(ə^2z)/( əxəy)
2.已知Z=ln(x+√(x^2+y^2),求(ə^2z)/( əx^2)和(ə^2z)/ ( əxəy)

1.Z=x^3siny+y^3sinx
əZ/əx=3x^2siny+y^3cosx
(ə^2z)/( əxəy)=(ə(əZ/əx))/əy=3x^2cosy+3y^2cosx
2.Z=ln(x+√(x^2+y^2))
əZ/əx=((x+√(x^2+y^2))^(-1))(1+(1/2)((x^2+y^2)^(-1/2))*2x)=(x^2+y^2)^(-1/2)
(ə^2z)/( əx^2)=(ə(əZ/əx))/əx=(-1/2)((x^2+y^2)^(-3/2))*2x
=x/(x^2+y^2)^(3/2)
(ə^2z)/ ( əxəy)=(ə(əZ/əx))/əy=y/(x^2+y^2)^(3/2)

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