题目

若z=f(x,y),x=u+v,y=u-v,则(partial^2z)/(partial upartial v)=(partial^2z)/(partial x^2)+(partial^2z)/(partial y^2)。() bigcircA.错 bigcircB.对

若z=f(x,y),x=u+v,y=u-v,则$\frac{\partial^{2}z}{\partial u\partial v}=\frac{\partial^{2}z}{\partial x^{2}}+\frac{\partial^{2}z}{\partial y^{2}}$。() $\bigcirc$A.错 $\bigcirc$B.对

题目解答

答案

计算一阶偏导数： $\frac{\partial z}{\partial u} = \frac{\partial z}{\partial x} + \frac{\partial z}{\partial y}, \quad \frac{\partial z}{\partial v} = \frac{\partial z}{\partial x} - \frac{\partial z}{\partial y}$ 计算二阶混合偏导数： $\frac{\partial^2 z}{\partial u \partial v} = \frac{\partial}{\partial v}\left(\frac{\partial z}{\partial u}\right) = \frac{\partial^2 z}{\partial x^2} - \frac{\partial^2 z}{\partial y^2}$ 与题目给定表达式比较，发现不相等。 答案： $\boxed{A}$。