1. See, it is nothing but the good-old chain rule.

2. So, we have to use the chain rule.

3. Our derivation of the chain rule contains one flaw.

4. I've seen this one before in the chain rule.

5. The other method is using the chain rule.

6. And now I'm going to use the chain rule.

7. Then by chain rule, dpA/dp dpA/dP. Constant temperature.

8. Two proving method for Chain rule of analytic function.

9. Well, we can use the chain rule.

10. what does the chain rule tell us?

11. The chain rule tells us, so we will want to differentiate - -- the formula for a with respect to theta holding a constant.http://

12. Well, we can answer that. The chain rule is something like this.

13. OK, this guy, by the chain rule, is the rate of change of f if I take x and y to be functions of t.

14. Expect one about a min/max problem, something about Lagrange multipliers, something about the chain rule and something about constrained partial derivatives.

15. I'm really just using that so I don't need to use the chain rule a billion times and doing derivatives.

16. Well, we could use differentials, like we did here, but we can also keep using the chain rule.

17. Well, of course we know the answer because that's a special case of the chain rule.

18. OK, this is only true for an ideal gas, and we went through that mathematically where the, with a chain rule.

19. In fact, if you have several substitutions to do, you can always arrange to use one chain rule at a time.

20. OK, and we can find this one from the constraints as we've een at the beginning either by differentiating the constraint, or by using the chain rule on the constraint.