Differentiate `sin^(-1)((2^(x+1))/(1+4^x))` with respect to `x`

Explanation

\begin{aligned}
&y=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^{x}}\right) \\
&y=\sin ^{-1}\left(\frac{2 \times 2^{x}}{1+\left(2^{2}\right)^{x}}\right) \\
&2^{x}=\tan \theta \Rightarrow \theta=\tan ^{-1}\left(2^{x}\right) \\
&y=\sin ^{-1}\left(\frac{2 \times \tan ^{2} \theta}{1+\tan ^{2} \theta}\right) \\
&y=\sin ^{-1}(\sin 2 \theta) \\
&y=2 \theta \\
&y=2 \tan ^{-1}\left(2^{x}\right) \\
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