Simplifying this differential using product rule?

[climbon]

Hi, I am trying to simplify this;

$$x \frac{\partial}{\partial x} W(x,y) - \frac{\partial}{\partial x} (xW(x,y))$$

Am I correct in thinking I can do this with the product rule, as;

$$\frac{\partial}{\partial x} (xW(x,y)) = \left( \frac{\partial x}{\partial x}\right) W(x,y) + x \frac{\partial W(x,y)}{\partial x} \\ =W(x,y) + x \frac{\partial W(x,y)}{\partial x}$$

Giving the whole thing as;

$$x \frac{\partial W(x,y)}{\partial x} - W(x,y) - x \frac{\partial W(x,y)}{\partial x}=W$$

Is this correct??

Thanks

 

[tiny-tim]

hi climbon!

$$x \frac{\partial W(x,y)}{\partial x} - W(x,y) - x \frac{\partial W(x,y)}{\partial x}=W$$

Is this correct??

Thanks

yes!