设方程\(z^2+y^2+z^2 = 4z\)确定函数\(z=z(x,y)\)，则\( { { {\partial ^2}z} \over {\partial {x^2}}} =\)
A: \( { { { { (2 - z)}^2} + {x^2}} \over { { {(2+ z)}^3}}}\)
B: \( { { { { (2 - z)}^2} + {x^2}} \over { { {(2 - z)}^3}}}\)
C: \( { { { { (2 - z)}^2} -{x^2}} \over { { {(2 - z)}^3}}}\)
D: \( { { { { (2 + z)}^2} + {x^2}} \over { { {(2 - z)}^3}}}\)
A: \( { { { { (2 - z)}^2} + {x^2}} \over { { {(2+ z)}^3}}}\)
B: \( { { { { (2 - z)}^2} + {x^2}} \over { { {(2 - z)}^3}}}\)
C: \( { { { { (2 - z)}^2} -{x^2}} \over { { {(2 - z)}^3}}}\)
D: \( { { { { (2 + z)}^2} + {x^2}} \over { { {(2 - z)}^3}}}\)
举一反三
- 设方程\({x^2} + {y^2} + {z^2} = 2Rx\)确定函数\(z=z(x,y)\)，则\( { { \partial z} \over {\partial x}}=\) A: \( { { \partial z} \over {\partial x}} = { { R +x} \over z}\) B: \( { { \partial z} \over {\partial x}} =- { { R +x} \over z}\) C: \( { { \partial z} \over {\partial x}} = { { R - x} \over z}\) D: \( { { \partial z} \over {\partial x}} =- { { R - x} \over z}\)
- 设方程\({sinz} - x^2yz = 0\)确定函数\(z=z(x,y)\)，则\( { { \partial z} \over {\partial x}}=\) A: \( { { 2xyz} \over {\cos z - {x^2}y}}\) B: \( { { 2xyz} \over {\cos z + {x^2}y}}\) C: \( { { xyz} \over {\cos z - {x^2}y}}\) D: \( { { 2xy} \over {\cos z - {x^2}y}}\)
- 9. 已知函数$z=z(x,y)$由${{z}^{3}}-3xyz={{a}^{3}}$确定，则$\frac{{{\partial }^{2}}z}{\partial x\partial y}=$（ ） A: $\frac{z({{z}^{4}}-2xy{{z}^{2}}-{{x}^{2}}{{y}^{2}})}{{{({{z}^{2}}-xy)}^{3}}}$ B: $\frac{z({{z}^{4}}-2xy{{z}^{2}}-xy)}{{{({{z}^{2}}-xy)}^{2}}}$ C: $\frac{z({{z}^{3}}-2xyz-{{x}^{2}}{{y}^{2}})}{{{({{z}^{2}}-xy)}^{3}}}$ D: $\frac{z({{z}^{3}}-2xy{{z}^{2}}-{{x}^{2}}y)}{{{({{z}^{2}}-xy)}^{3}}}$
- 设\(z = z\left( {x,y} \right)\)是由方程\(2{x^2} + {y^2} + {z^2} - 2z = 0\)确定的隐函数，则\( { { \partial z} \over {\partial x}}=\)（ ）。 A: \( { { 2x} \over {1 - z}}\) B: \( { { 2x} \over {z - 1}}\) C: \({z \over {1 - y}}\) D: \({z \over {y - 1}}\)
- 由方程\({z^3} - 3xyz = {a^3}\)所确定的隐函数\(z= f(x,y)\)的偏导数\( { { \partial z} \over {\partial x}} = \) A: \( { { yz} \over { { z^2} - xy}}\) B: \(- { { yz} \over { { z^2} - xy}}\) C: \( { { yz} \over { { z^2} +xy}}\) D: \(- { { yz} \over { { z^2}+xy}}\)