Can I Take the X Component Out When Differentiating with Respect to Z?

[Oblio]

I'm confused on a procedural idea...

If I'm doing the cross product of a gradient and 'the x component of a force' , so:

$$\nabla X F(x) = \frac{\partial}{\partial z} Fy$$

and Fy = x..

even though I am differentiating with respect to z , I am solving for an x component, which means I can not take x out with the other constants... yes? (if there were some)

I guess I'm confused because I know this shouldn't = 0 afterwards, but I'm not differentiating wrt z, so I'm trying to figure out why.


Thanks a lot !

(F(z) is 0 in case your wondering why its only Fy.)

 

[Astronuc]

Is one looking at something like this?

$$det \[ \left[ \begin{array}{ccc}<br /> \hat{x} & \hat{y} & \hat{z} \\\<br /> \frac{\partial}{\partial{x}} & \frac{\partial}{\partial{y}} & \frac{\partial}{\partial{z}} \\\<br /> F_x & F_y & F_z \end{array} \right]\]$$

 

[Oblio]

yes I am...
thats how I set up the equation, but I don't know if I may take x out or not.