The partial derivatives position [closed]
Is $\displaystyle \frac{\partial}{\partial x} \ x=x\frac{\partial}{\partial x}=1$?
Solution 1:
No. In the way you wrote, they should be intended as operator acting on something. So the first one is $$ \partial_x(xu) = u + x\partial_x u $$ while the second is $$ x\partial_x u. $$ Note so that $\partial_x x - x \partial_x = 1$, as operators acting on something.