# Math Help - Derivative question

1. ## Derivative question

Hello!

I am having trouble deriving y = cot(arctan(x))

I got dy/dx = [-1+tan^2(arctan(x))]/[tan^2(arctan(x))(1+x^2)]

I used the chain rule for the overall equation, and I also used

Does this look correct? Or am I way off? Perhaps, can this be simplified further?

Any help is much appreciated,

Dranalion

2. $cot(arctan(x)) = \frac{1}{tan(arctan(x))} = ?$

3. Using this, I got:

dy/dx = [(-sec^2(arctan(x))/(1+x^2)] / [tan^2(arctan(x)]

I seem even more tangled!

Am I on the right track? Can this be simplified further?

Any help much appreciated

4. You should recall that by definition, $tan(arctan(x)) = arctan(tan(x)) = x$

5. So does: y = cot(arctan(x))

dy/dx = -1/x^2

Sound right?

6. Yep.