y=2^sin ^-1 x × e^cos ^-1(x-2), then (d y)/(d x) is

$y=2^{\sin ^{-1} x} . e^{\cos ^{-1}(x-2)}$

$\log y=\sin ^{-1} × \log 2+\cos ^{-1}(x-2)$

$\frac{1}{y} . \frac{d y}{d x}=\frac{\log 2}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-(x-2)^2}}=\frac{\log 2}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-x^2-4+4 x}}$

= answer is none of these.

Hence (4) is correct answer.