Thread: 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

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

You should recall that by definition,

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

dy/dx = -1/x^2


Sound right?

Yep.