Since y = sin − 1 ( x ) {\displaystyle y=\sin ^{-1}({\sqrt {x}})} can be written as y = sin − 1 ( u ) {\displaystyle y=\sin ^{-1}(u)} with u = x {\displaystyle u={\sqrt {x}}} and d d u sin − 1 ( u ) = 1 1 − u 2 {\displaystyle {\frac {d}{du}}\sin ^{-1}(u)={\frac {1}{\sqrt {1-u^{2}}}}} , the chain rule gives
