设λ是正常数，并且xy^λdx+x^λydy是其个函数u(x,y)的全微分，则λ=___________.
举一反三
- 设函数y＝y（x）由方程2^xy＝x＋y所确定，则dy|x＝0＝（） A: （ln2－1）dx B: （l－ln2）dx C: （ln2－2）dx D: ln2dx
- 设f(u)连续，且du(x，y)=f(xy)(ydx+xdy)，则u(x，y)=______．
- 设y=x^(x)(x>0)则函数y的微分dy=?
- 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: \(dz = {\left( {xy} \right)^x}\left( {1 + \ln xy} \right)dx + { { x { { \left( {xy} \right)}^x}} \over y}dy\)
- 验证下列P(x,y)dx+Q(x,y)dy在全平面内是某个函数u(x,y)的全微分，并求此原函数u(x,y)：[tex=8.929x1.214]+Bv9d3kvB+awCTj+A3DPy76f9H6PKhnxrvjERsPgQUKstjkYN3M6bUOILXi9vjL2[/tex]