If $y=\sin x+e^x$, then $\frac{d^2 x}{d y^2}$ equals

$\frac{\sin x-e^x}{\left(\cos x+e^x\right)^3}$

We have,

$y=\sin x+e^x $

$\Rightarrow \frac{d y}{d x}=\cos x+e^x $

$\Rightarrow \frac{d x}{d y}=\left(\cos x+e^x\right)^{-1}$

$\Rightarrow \frac{d^2 x}{d y^2}=-\left(\cos x+e^x\right)^{-2}\left(-\sin x+e^x\right) \frac{d x}{d y}$

$\Rightarrow \frac{d^2 x}{d y^2}=\frac{\sin x-e^x}{\left(\cos x+e^x\right)^2} . \left(\cos x+e^x\right)^{-1}=\frac{\sin x-e^x}{\left(\cos x+e^x\right)^3}$