[WalrusMaximus]

I'm having trouble determining when to use: lnK = -(delta)G/RT vs dK/d(1/T) = (delta)H/R
My professor says I can use the first equation at any T but on homework the equation only works at 298K. He then said something like "the first equation tells you K at any T, the second tells you how K relates to T" what's the difference? Sounds like the same thing. 
I appreciate any help.
If a specific example would help, I'm referring to this. http://puu.sh/dpPaj/5e1f6701f4.png

[mjc123]

The first equation applies at any T, but you might only know ΔG° at 298K or some other specific temperature. If you know ΔH° (and assume it is temperature-independent), you can use the second equation to calculate K at any other temperature within reason.
Your second equation is not quite correct; it should be d(lnK)/d(1/T) = ΔH°/R

[Plontaj]

Nope.

d(lnK)/d(1/T) = ΔH°/R

The correct form is: d(lnK)/d(1/T) = -ΔH°/R

Van't Hoff isobar: d(lnK)/d(1/T)= -ΔH°/R at constant pressure is a derivative of the temperature of equation: lnK = -ΔG°/(RT) = -ΔH°/(RT) + ΔS°/R . To calculate lnK from van't Hoff isobar you need integrate this equation and need to know the integral constant = ΔS°/R.

Derivation:
ΔG° = ΔH° - TΔS°

lnK=-ΔH°/(RT) + ΔS°/R

d(lnK)/d(T) = ΔH°/(RT^2)

d(lnK)/d(1/T) = -ΔH°/(R)