求函数Z=ln(x+y2)的偏导数az/ax.az/ay及全微分.
问题描述:
求函数Z=ln(x+y2)的偏导数az/ax.az/ay及全微分.
答
ez/ex
=1/(x+y^2) *1
=1/(x+y^2)
ez/ey=1/(x+y^2)* (2y)
=2y/(x+y^2)
dz=ez/ex dx+ ez/ey dy
=1/(x+y^2) dx+ 2y/(x+y^2) dy