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 $\arcsin \left({\dfrac x a}\right)$ be the arcsine of $\dfrac x a$.

Then:
 * $\dfrac {\mathrm d \left({\arcsin \left({\frac x a}\right)}\right)} {\mathrm d x} = \dfrac 1 {\sqrt {a^2 - x^2}}$

Also see

 * Derivative of $\arccos \dfrac x a$


 * Derivative of $\arctan \dfrac x a$


 * Derivative of $\operatorname{arccot} \dfrac x a$


 * Derivative of $\operatorname{arcsec} \dfrac x a$


 * Derivative of $\operatorname{arccsc} \dfrac x a$