University of Florida/Egm4313/s12.team11.perez.gp/R1.4

Problem: Derive (3) and (4) from (2).

Given:

(2)

(3)

(4)

Solution:

First, let's solve for (3).

Recall that:

,

and

.

We can use this information to replace the differentiating terms accordingly.

After doing so, we get:

but knowing that , we can rearrange the terms to get .

Using this information in the previously derived equation, we find that:

.

Finally, after differentiating with respect to , we get:

.

Now, let's solve for (4).

Once again considering that , we can solve for (4) by differentiating

twice and then plugging it into (2).

Deriving twice, we find that:

After plugging this into (2), we see that:

.

Once we rearrange , we find that .

We can plug this in to the above equation to get the solution:

.