Could someone please tell me how can I use chain rule to show solution (1) in below paragraph holds?
Last time I asked someone gave me below answer:
But I don't understand why we have f '(x-t) instead of both du/dx and du/dt? Does f '(x-t) mean du/dt or du/dx (since chain rule says du/dx=du/dt * dt/dx and du/dt=du/dx * dx/dt)?
(I have used d because I did not have the correct character on the keyboard).
Thank you very much.
No. f' is the derivative of f (as a function of one variable), and now evaluate this function at x-t to give f'(x-t). Also, you need to keep track of what you are keeping constant in those partial derivatives when using the chain rule.
with respect to x (keeping t constant) gives
with respect to t (keeping x constant) gives