函数\(z = {x^y}\)的全微分为
A: \(dz = y{x^{y - 1}}dy + {x^y}\ln xdx\)
B: \(dz = y{x^{y - 1}}dx + {x^y}dy\)
C: \(dz = y{x^{y - 1}}dx + {x^y}\ln xdy\)
D: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
A: \(dz = y{x^{y - 1}}dy + {x^y}\ln xdx\)
B: \(dz = y{x^{y - 1}}dx + {x^y}dy\)
C: \(dz = y{x^{y - 1}}dx + {x^y}\ln xdy\)
D: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
举一反三
- 设视点为坐标原点，投影平面为z=d，则点p(x,y,z)的投影为（）。 A: (dx,dy,dz,z) B: (x,y,z,dz) C: (dx,dy,dz,1) D: (x,y,z,d)
- 函数\(z = {\left( {xy} \right)^x}\)的全微分为 A: \(dz = \left( { { {\left( {xy} \right)}^x} + \ln xy} \right)dx + x{\left( {xy} \right)^x}dy\) B: \(dz = \left( { { {\left( {xy} \right)}^x} + \ln xy} \right)dx + { { x { { \left( {xy} \right)}^x}} \over y}dy\) C: \(dz = {\left( {xy} \right)^x}\ln xydx + { { x { { \left( {xy} \right)}^x}} \over y}dy\) D: \(dz = {\left( {xy} \right)^x}\left( {1 + \ln xy} \right)dx + { { x { { \left( {xy} \right)}^x}} \over y}dy\)
- 函数z=exy当x=1, y=1, Dx=0.15, Dy=0.1时的全微分dz= .
- 方程xdy/dx＝yln（y/x）的通解为（）。 A: ln（y/x）＝1 B: ln（y/x）＝Cx＋1 C: ln（y/x）＝Cx<sup>2</sup>＋1 D: ln（y/x）＝Cx<sup>3</sup>＋1
- 设\(z = {e^ { { y \over x}}} + {x^y} + {y^x}\)，则\({z_x} = \) A: \({1 \over x}{e^ { { y \over x}}} + {x^y}\ln x + x{y^{x - 1}}\) B: \(- {y \over { { x^2}}}{e^ { { y \over x}}} + {x^y}\ln x + x{y^{x - 1}}\) C: \({e^ { { y \over x}}} + y{x^{y - 1}} + {y^x}\ln y\) D: \( - {y \over { { x^2}}}{e^ { { y \over x}}} + y{x^{y - 1}} + {y^x}\ln y\)