If $e^y(x+2)=10, $ then $\frac{d^2y}{dx^2}$ is equal to :

$\left(\frac{dy}{dx}\right)^2$ $\left(\frac{dy}{dx}\right)^3$ $\left(\frac{dy}{dx}\right)$ $-\left(\frac{dy}{dx}\right)^2$

$\left(\frac{dy}{dx}\right)^2$

The correct answer is Option (1) → $\left(\frac{dy}{dx}\right)^2$ $e^y(x+2)=10$ differentiating wrt x $e^y(x+2)\frac{dy}{dx}+e^y=0$ $(x+2)\frac{dy}{dx}+1=0⇒\frac{dy}{dx}=\frac{-1}{(x+2)}$ so $\frac{d^2y}{dx^2}=\frac{1}{(x+2)^2}=\left(\frac{dy}{dx}\right)^2$