$y=2^{\sin ^{-1} x} \times e^{\cos ^{-1}(x-2)}$, then $\frac{d y}{d x}$ is

$\frac{y \log 2}{\sqrt{1-x^2}}$ $\frac{y \log (2 / e)}{\sqrt{1-x^2}}$ $\frac{y-1}{\sqrt{1-x^2}}$ none of these

none of these

$y=2^{\sin ^{-1} x} . e^{\cos ^{-1}(x-2)}$ $\log y=\sin ^{-1} × \log 2+\cos ^{-1}(x-2)$ $\frac{1}{y} . \frac{d y}{d x}=\frac{\log 2}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-(x-2)^2}}=\frac{\log 2}{\sqrt{1-x^2}}-\frac{1}{\sqrt{1-x^2-4+4 x}}$ = answer is none of these. Hence (4) is correct answer.