When do you use the partial symbol vs. The normal derivative symbol? For example, I’m trying to write out the derivative of a function f with parts a and b that are respectively dependent on u and v, which are both dependent on x and t. Since a is only dependent on u and b only on v, do I write out the derivative of u with respect to a as a regular derivative, not a partial?
Also, since the function is f(x,t)=a(x+ct) + b(x-ct), do we just write out partial of f with respect to x as starting with the partial of a with respect to u ... The reason for this question is that the formula for partials is the derivative of f with respect to u... but I am wondering if here a and b are acting kind of like f, so we just start with a and b in front?
Hope that this question is worded clearly enough! Many thanks.