How can I prove this relation between derivatives? [closed]

Question

Consider coaixialcable with TEM. Nonstatic fields are being considered, i.e situation obeys $\nabla \times \mathbf {E}=-\frac{\partial \mathbf{B} }{\partial t} $

If I let a eletric field be described as $\textbf{E}=[E^+(z-ct)+E^-(z+ct)]\hat s $

Can someone help me on how to show that : $\frac{\partial E^{\pm} }{\partial z}=\frac{1}{\mp c}\frac{\partial E^{\pm} }{\partial t}$

Answer 1

In just the chain rule. For example $$ \partial_x \sin(x-ct)= \cos(x-ct)\\ \partial_t \sin(x-ct)= -c\cos(x-ct) $$