Question

When we differentiate an equation,
dy/dx=f'(x) we say that we have differentiated f(x) with respect to x'.
Why does with respect to x' mean?

Answer 1

No one should say "with respect to x'". It should be just "with respect to x". This is often abbreviated to "wrt x". It means only that x is the variable of interest and, unless otherwise stated, is the ONLY variable of interest.

Answer 2

What do we mean by of interest and

Answer 3

And only of interest and what if its no the inly one of interst