Why is the partial derivative of Lx with respect to x zero

[M. next]

Why is it that partial derivative of Lx wrt x is zero?
where: Lx (Angular momentum along x)

Yes and for further info. they wrote beside this that dLx/dx =d(yPz - zPy)/dx = 0

I guess it resulted from some determinant but I just could not figure it out.

(This was a snatch of a problem in Poisson's Bracket)

 

[Infinitum]

Yes and for further info. they wrote beside this that dLx/dx =d(yPz - zPy)/dx = 0

Do you know multivariable calculus? y and z are constants when differentiated with respect to x. Hence, the result.