Question

How do you find the derivative of `arctan(1/x)`?

Answer 1

`-1/(1+x^2)`

Explanation:

Know ahead of time that `d/dxcot^-1(x)=-1/(1+x^2)`:

We see that:

`y=tan^-1(1/x)`

`tan(y)=1/x`

`1/tan(y)=1/(1/x)`

`cot(y)=x`

`y=cot^-1(x)`

Thus:

`dy/dx=-1/(1+x^2)`