#$&*
course Phy 231
6/28 630
This might look more natural to you if you use plain, unadorned letters in place of u2, v1 and u1. Let's use a, x and b, respectively. The expression becomes a / (x - b)
and the derivative is
-a / (x - b)^2.
There are two ways to see the derivative:
The function is the product of the constant a and the function (x - b)^(-1). The derivative of the latter is (x - b) ' * (-1) ( x - b)^(-2).
The function is of the form f / g with f = a, g = (x - b), so the derivative is ( (a) ' ( x - b) - a * (x - b) ' ) / (x - b) ^ 2 = (0 - a) / (x - b)^2 = -a / (x - b)^2.
Either way it should now be clear that the derivative of u2 / (v1 - u1) = - u2 / (v1 - u1)^2
################
I do see now. Sorry about that if I would have wrote it like u2*(v1-u1)^-1, then I would have seen it much better, (-1)u2*(v1-u1)^(-1-1)*1=-u2/(v1-u1)^-2
#####################
"
The use of subscripted variables makes this a little harder to see.
Check the expanded discussion at the link:
&#Please see the following link for more extensive commentary on this lab. You should read over all the commentary and note anything relevant. Give special attention to any comments relevant to notes inserted into your posted work. If significant errors have occurred in your work, then subsequent results might be affected by those errors, and if so they should be corrected.
Expanded Commentary
Please respond by submitting a copy of this document by inserting revisions and/or self-critiques and/or questions as appropriate. Mark you insertions with #### and use the Submit Work Form. If a title has been suggested for the revision, use that title; otherwise use an appropriate title that will allow you to easily locate the posted response at your Access Page. &#
#$&*