What is the derivative of ${(tan x)}^{- 1}$ $(tanx)^-1$ ?

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Answer 1 · 2018-03-08T15:04:59

$- {csc}^{2} (x)$ $-csc^2(x)$

We have:

$\frac{d}{d x} ({(tan (x))}^{- 1})$ $d/dx((tan(x))^-1)$

Using, ${(tan (x))}^{- 1} = cot (x)$ $(tan(x))^-1=cot(x)$ , we get

$\frac{d}{d x} (cot (x))$ $d/dx(cot(x))$

$= - {csc}^{2} (x)$ $=-csc^2(x)$

Source:

What is the derivative of (tanx)−1(tanx)^-1?