1.求下列函数的全微分：(1)z=3x^2y+(x)/(y); (2)z=sin(xcos y); (3)u=x^yz.2.求函数z=ln(2+x^2+y^2)在x=2，y=1时的全微分.3.设f(x,y,z)=sqrt[x]((x)/(y)),求df(1,1,1).

1. **全微分计算** (1) $ z = 3x^2y + \frac{x}{y} $ $ dz = \left(6xy + \frac{1}{y}\right)dx + \left(3x^2 - \frac{x}{y^2}\right)dy $ (2) $ z = \sin(x\cos y) $ $ dz = \cos(x\cos y)\cos y \, dx - x\sin y\cos(x\cos y) \, dy $ (3) $ u = x^{yz} $ $ du = yzx^{yz-1}dx + x^{yz}z\ln x \, dy + x^{yz}y\ln x \, dz $ 2. **函数 $ z = \ln(2 + x^2 + y^2) $ 在 $ x=2, y=1 $ 处的全微分** $ dz = \frac{4}{7}dx + \frac{2}{7}dy $ 3. **函数 $ f(x,y,z) = \sqrt[x]{\frac{x}{y}} $ 在 $ (1,1,1) $ 处的全微分** $ df(1,1,1) = dx - dy $ \[ \boxed{ \begin{array}{ll} 1. & (1) \, dz = \left(6xy + \frac{1}{y}\right)dx + \left(3x^2 - \frac{x}{y^2}\right)dy \\ & (2) \, dz = \cos(x\cos y)\cos y \, dx - x\sin y\cos(x\cos y) \, dy \\ & (3) \, du = yzx^{yz-1}dx + x^{yz}z\ln x \, dy + x^{yz}y\ln x \, dz \\ 2. & dz = \frac{4}{7}dx + \frac{2}{7}dy \\ 3. & df(1,1,1) = dx - dy \\ \end{array} } \]