If $e^y(x+2)=10, $ then $\frac{d^2y}{dx^2}$ is equal to :
Answer & explanation
Correct answer: option 1
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 $\frac{d^2y}{dx^2}=\frac{1}{(x+2)^2}=\left(\frac{dy}{dx}\right)^2$