Derivative of Arcsine Function/Corollary

Corollary to Derivative of Arcsine Function
Let $a \in \R$ be a constant

Let $x \in \R$ be a real number such that $x^2 < a^2$.

Let $\map \arcsin {\dfrac x a}$ be the arcsine of $\dfrac x a$.

Then:
 * $\dfrac {\map \d {\map \arcsin {\frac x a} } } {\d x} = \dfrac 1 {\sqrt {a^2 - x^2} }$

Also see

 * Derivative of $\arccos \dfrac x a$


 * Derivative of $\arctan \dfrac x a$


 * Derivative of $\arccot \dfrac x a$


 * Derivative of $\arcsec \dfrac x a$


 * Derivative of $\arccsc \dfrac x a$