I'm looking for a general method to evaluate expressions of the form
$\frac{\mathrm{d}(u^v)}{\mathrm{d}u}\text{ and }\frac{\mathrm{d}(u^v)}{\mathrm{d}v}\;.$
I know that the answers to these are, respectively, $u^{v-1}v$ and $u^v\mathrm{ln}u$, but am unsure of how to obtain them, and how the chain rule applies here.
I'd be very grateful of any enlightenment.
With very many thanks,
Froskoy.