This seems to be a "trick question" set by the teacher, or a typo.
If we had information that x was dependant on w as x = x(w)
then df/dw = (df/dx)*(dx/dw)
and we would calculate the overall result as
(57x^2 + 12x + 12)*(dx/dw)
However there is no information of any such dependancy
so we assume (dx/dw) = 0 and so df/dw = 0
We do not write all this out every time, but just note that w is not a variable.
Hope that helps,
Regards - Ian
