Taking Differentials to Find Partial Derivative

[jamjar]

Hi,
I'm trying to take differentials of the following equation

$$(p + \frac{a}{{V^2 }})(V - b) = C$$

in order to find the partial derivative $$\frac{{\partial p}}{{\partial V}}$$

I know there's an easier way to do it but I have to take differentials.
I'm just not sure how to deal with the brackets without multiplying out (I can't rearrange the equation).

Any hints welcome.

 

[HallsofIvy]

Use the product rule!

 

[jamjar]

How do I do that with differentials?
I end up with crazy results.

 

[Physics Monkey]

You "can't" rearrange the equation, as in the problem won't let you? The product rule for differentials is $$d(fg) = g df + f dg$$.

 

[jamjar]

If I use that product rule I end up with a free floating $$p$$ in my equation where I know that $$\frac{{\partial p}}{{\partial V}}$$ doesn't have a term in $$p$$

 

[Physics Monkey]

Yes, you then have to solve for p in terms of V using the original equation. This I why I don't undestand why you can't just solve for p in terms of V from the start since you have do it eventually anyway.