determine and
am I right in thinking that:
and if so, where do I go from there? I don't suppose i can do this by diff w.r.t x:
giving me the rather dodgy looking answer:
and for the other one, by diff w.r.t y:
thanks, i hope at least the first step is right....
I don't know how often it appears in pure Math, but the notation is common in Thermodynamics. Functions are typically given in terms of three "extensive" variables such as volume, temperature, and pressure. (V, T, and P). The derivative is the derivative of the internal energy function U(P, V, T)with respect to the temperature at constant pressure. The volume is allowed to change as a function of T in this case, so technically this isn't a partial derivative at all though the derivative operation on the function U is calculated as if it were a partial derivative.
-Dan
yer i like this, thanks! I'll have to prove that formula (i can't just quote it) but i've done that so the first one is done. However, for i don't see how i can use the same formula as the variable being differentiated, y, is now on the bottom, so isn't a different one is needed?
ie
it's a well-known rule, you can just use it. i very much doubt you would be required to prove it
use the chain rule, as JaneBennet did.but i've done that so the first one is done. However, for i don't see how i can use the same formula as the variable being differentiated, y, is now on the bottom, so isn't a different one is needed?
ie
so what is ?
note: you will not need the product rule here, since x is considered a constant