If y = (1 + x)y + sin^ - 1 ( sin^ 2 x) , then (dy)/(dx) at x = 0 is

$\dfrac{dy}{dx} = {\left(1 + x\right)}^{y}\left\{\dfrac{y}{1 + x} + \ln \left(1 + x\right) ⋅ \dfrac{dy}{dx}\right\} + \dfrac{\sin 2x}{\sqrt{1 - sin^{4}\left(x\right)}}$
Putting $x = 0$ & $y = 1$, we get,

$\dfrac{dy}{dx} = 1\left\{1 + \ln \left(1\right) . \dfrac{dy}{dx}\right\} + 0 = 1$