\(y = {\sin ^{ - 1}}x\) is defined for the domain \( - 1 \le x \le 1\)
\(\dfrac{{dy}}{{dx}} = \dfrac{1}{{\sqrt {1 - {x^2}} }}\) for the domain \( - 1 < x < 1\)
\(y = {\sin ^{ - 1}}\dfrac{x}{a}\)is defined for the domain \( - a \le x \le a\)
\(\dfrac{{dy}}{{dx}} = \dfrac{1}{{\sqrt {{a^2} - {x^2}} }}\) is defined for the domain \( - a < x < a\)
\(y = {\cos ^{ - 1}}x\) for the domain \( - 1 \le x \le 1\)
\(\dfrac{{dy}}{{dx}} = - \dfrac{1}{{\sqrt {1 - {x^2}} }}\) is defined for the domain \( - 1 < x < 1\)
\(y = {\cos ^{ - 1}}\dfrac{x}{a}\) is defined for the domain \( - a \le x \le a\)
\(\dfrac{{dy}}{{dx}} = - \dfrac{1}{{\sqrt {{a^2} - {x^2}} }}\) is defined for the domain \( - a < x < a\)
\(y = {\tan ^{ - 1}}x\) is defined for the domain \( - \infty < x < \infty \)
\(\dfrac{{dy}}{{dx}} = \dfrac{1}{{1 + {x^2}}}\) is defined for the domain \( - \infty < x < \infty \)
\(y = {\tan ^{ - 1}}\dfrac{x}{a}\) is defined for the domain \( - \infty < x < \infty \)
\(\dfrac{{dy}}{{dx}} = \dfrac{a}{{{a^2} + {x^2}}}\) is defined for the domain \( - \infty < x < \infty \)