Question

What is the derivative of `f(x) = cot(x)`?

Answer 1

Derivative of `cot(x)` is equal to `-csc^2(x)`.

Explanation:

We know that `cot(x) = 1/tan(x)` so `f'(x) = 1/tan(x)dx`

We can use the quotient rule to solve for the derivative. The quotient rule states:

`d(g(x)/(h(x))) = ((g'(x)h(x) - g(x)h'(x))/g(x)^2)dx`

in our case,

`g(x) = 1`
`h(x) = tan(x)`
`g'(x) = 0`
`h'(x) = sec^2(x)`

Let's plug these values back into the quotient rule:

`(0 * tan(x) - 1 * sec^2(x))/tan^2(x) = -sec^2(x)/tan^2(x) = - csc^2(x)`