help with total differentiation

Hello,

If w=f(ax+by) I am asked to show -please read w[x] as partial derivative fo w w.r.t.x- that: bw[x]-aw[y]=0 this tells me that the difference of a ccahnge in the coordinates of a points on on a curve in different directiosn will be zero (though pls dont be too harsh if I have - which i probably have - got the whole geometry thing wrong

i am given as a hint to let ax +by = z

i can totally differentiate this : dz = adx + bdy

and totally differentiated w: dw = w[x]dx + w[y]dy but don't know hyow to come up with the desried result.

pls help