Hello, NBrunk!

Do you know the derivative of the inverse cotangent?

If you do, exactly *where* is your difficulty?

Differentiate: . . .

. . and we want: .

. .

. .

Therefore: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here's an "eyeball" solution . . . which takes a bit of *Thinking.*

The first term is

This is an angle whose cotangent is

That is: .

Its right triangle looks like this:

Code:

* B
* |
* |
* | 1
* |
* θ |
A * - - - - - - - - *
t

The second term is: .

This is an angle whose cotangent is: .

Look at the diagram above . . . Can you find such an ngle?

With a little mental acrobatics, we see that it is angle , the "other" angle!

You see: . . . . This sum is 90°, a constant.

So we did all that work to differentiate a *constant!*