University of Florida/Egm4313/

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






First, let's solve for (3).

Recall that:




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: