$\begin{aligned} & y=\sin ^{-1}\left(\frac{5 x+12 \sqrt{1-x^2}}{13}\right) \\ & \Rightarrow y=\sin -1\left(x \cdot \frac{5}{13}+\frac{12}{13} \sqrt{1-x^2}\right)\end{aligned}$
[let $x=\sin \theta$ i.e., $\theta=\sin ^{-1} X$ and $\cos \theta=\sqrt{1-X^2}$
also let $\frac{5}{13}=\cos \alpha$ i.e. $\left.\frac{12}{13}=\sin \alpha\right]$
$\begin{aligned} & \Rightarrow y=\sin ^{-1}(\sin \theta \cdot \cos \alpha+\cos \theta \cdot \sin \alpha) \\ & \Rightarrow y=\sin -1 \sin (\theta+\alpha) \\ & \Rightarrow \frac{d y}{d x}=\frac{1}{\sqrt{1-x^2}}+0=\frac{1}{\sqrt{1-x^2}}\end{aligned}$