I disagree with the first sentence. Since my disagreement hinges on the difference between partial and total derivatives I hope it is broadly interesting.
If q is a function of c, then h becomes a function of one independent variable, and your use of partials here doesn’t make sense, because you can’t hold c constant while changing q or vice versa.
You are making me feel old. My notation was orthodox in 1958. Indeed, in A Course Of Pure Mathematics, Tenth Edition, section 157, Hardy writes:
The distinction between the two functions is adequately shown by denoting the first by frac{df}{dx} and the second by frac{partialf}{partialx}, in which case the theorem takes the form frac{df}{dx}=frac{partialf}{partialx}frac{partialf}{partialy}frac{dy}{dx}; though this notation is also open to objection, in that it is a little misleading to denote the functions
\}) and
) whose forms as functions of x are quite different from one another, by the same letter f in frac{df}{dx} and frac{partialf}{partialx}.
I think your notation is still orthodox, or at least fairly common, nowadays. Wikipedia uses it on its total derivative page, for example, and it seems familiar to me.
If q is a function of c, then h becomes a function of one independent variable, and your use of partials here doesn’t make sense, because you can’t hold c constant while changing q or vice versa.
I thought that this was the kind of situation partial derivatives are there for. AlanCrowe’s just applied the multivariable chain rule, if I’m getting it right.
If q is a function of c, then h becomes a function of one independent variable, and your use of partials here doesn’t make sense, because you can’t hold c constant while changing q or vice versa.
You are making me feel old. My notation was orthodox in 1958. Indeed, in A Course Of Pure Mathematics, Tenth Edition, section 157, Hardy writes:
The distinction between the two functions is adequately shown by denoting the first by frac{df}{dx} and the second by frac{partialf}{partialx}, in which case the theorem takes the form frac{df}{dx}=frac{partialf}{partialx} frac{partialf}{partialy}frac{dy}{dx}; though this notation is also open to objection, in that it is a little misleading to denote the functions
I think your notation is still orthodox, or at least fairly common, nowadays. Wikipedia uses it on its total derivative page, for example, and it seems familiar to me.
I thought that this was the kind of situation partial derivatives are there for. AlanCrowe’s just applied the multivariable chain rule, if I’m getting it right.
Thanks, you (and Alan) are right. Sorry, it’s been a while.