函数z=ln(1 x2 y2)当x=1, y=2时的全微分dz= .
举一反三
- 函数z=ln(1 x2 y2)当x=1, y=2时的全微分dz= .
- 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: \(dz = y{x^{y - 1}}dy + {x^y}dx\)
- 函数z=exy当x=1, y=1, Dx=0.15, Dy=0.1时的全微分dz= .
- 函数\(z = \ln \left( { { x^2} + {y^2}} \right)\)在\(x = 2,y = 1\)时的全微分为 A: \(0.8dx+0.4dy\) B: \(0.8dx-0.4dy\) C: \(8dx+4dy\) D: \(8dx-4dy\)
- 4.已知二元函数$z(x,y)$满足方程$\frac{{{\partial }^{2}}z}{\partial x\partial y}=x+y$，并且$z(x,0)=x,z(0,y)={{y}^{2}}$，则$z(x,y)=$（ ） A: $\frac{1}{2}({{x}^{2}}y-x{{y}^{2}})+{{y}^{2}}+x$ B: $\frac{1}{2}({{x}^{2}}{{y}^{2}}+xy)+{{y}^{2}}+x$ C: ${{x}^{2}}{{y}^{2}}+{{y}^{2}}+x$ D: $\frac{1}{2}({{x}^{2}}y+x{{y}^{2}})+{{y}^{2}}+x$