Question

What is the derivative of `cot^-1(x)`?

Answer 1

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

Explanation:

Let `y=arccot(x)`
then
`cot(y)=x`
so

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

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

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