So I'm trying to understand some of these physics concepts we've been going over in class. I'm supposed to find some partial's but I don't think I'm quite understanding the process/mathematics behind it.
Given I have: $$m=pq \\ a\sin(p-p)=q \\ b\cos(q+q)=p $$ What I've done so far (which I think is right) $$ \mathrm{d}q = a\cos(p-p)(\mathrm{d}p-\mathrm{d}p) \\ \mathrm{d}p= -b\sin(q+q)(\mathrm{d}q+\mathrm{d}q) $$ I'm supposed to find $\left(\frac{\partial(p)}{\partial(q)}\right)_m$, $\left(\frac{\partial(p)}{\partial(q)}\right)_a$
I know the answers for these specific ones are :
$$ \left(\frac{\partial(p)}{\partial(q)}\right)_m=\frac {-p}{q} \\ \left(\frac{\partial(p)}{\partial(q)}\right)_a= \frac {1}{a\cos (p-1)} $$
I'm just not sure on the math to get to those answers. I was wondering if someone could help me understand these so I can apply it to more examples I have to do.
Thanks in advance!