Derivatives of Inverse Secant and Tangent

The domain of $\sec^{-1}(x)$ leads to a simpler derivative without absolute value, unlike the more complex derivative of $\tan^{-1}(x)$.

Both $\sec^{-1}(x)$ and $\tan^{-1}(x)$ have identical domains, resulting in derivatives with the same level of complexity and form.

The domain of $\sec^{-1}(x)$ ($|x| \geq 1$) results in a more complex derivative with $|x|$, while $\tan^{-1}(x)$’s domain allows for a simpler form.

The domain of $\sec^{-1}(x)$ causes its derivative to be undefined for all real numbers, while $\tan^{-1}(x)$’s derivative is defined everywhere.