计算 z=yln(xy)+e^(xy) 的两个偏导数
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z=yln(xy)+e^(xy)
∂z/∂x
=∂/∂x[ yln(xy)+e^(xy)]
=y.∂/∂x[ln(xy)] + e^(xy).∂/∂x(xy)
=y.[y/(xy)] + e^(xy).(y)
=xy + y.e^(xy)
z=yln(xy)+e^(xy)
∂z/∂y
=∂/∂y[ yln(xy)+e^(xy)]
= y.∂/∂y[ln(xy)] +ln(xy).∂/∂y(y)+e^(xy).∂/∂y(xy)
= y.[x/(xy)] +ln(xy).(1)+e^(xy).(x)
=y^2 +ln(xy) +xe^(xy)
∂z/∂x
=∂/∂x[ yln(xy)+e^(xy)]
=y.∂/∂x[ln(xy)] + e^(xy).∂/∂x(xy)
=y.[y/(xy)] + e^(xy).(y)
=xy + y.e^(xy)
z=yln(xy)+e^(xy)
∂z/∂y
=∂/∂y[ yln(xy)+e^(xy)]
= y.∂/∂y[ln(xy)] +ln(xy).∂/∂y(y)+e^(xy).∂/∂y(xy)
= y.[x/(xy)] +ln(xy).(1)+e^(xy).(x)
=y^2 +ln(xy) +xe^(xy)
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