Question

2nd derivative of 4x^2 - 2y^2 =9​

Answer 1

Answer:

The answer is $-\dfrac{9}{y^3}$

Step-by-step explanation:

Given equation is $4x^2-2y^2=9$

Differentiate both sides w.r.t. $x$

                          $\Rightarrow 8x-4y\dfrac{dy}{dx}=0\\\\\Rightarrow \dfrac{dy}{dx}=\dfrac{8x}{4y}=\dfrac{2x}{y}$

Differentiate again using quotient rule w.r.t. x

                          $\Rightarrow \dfrac{d^2y}{dx^2}=2(\dfrac{y(1)-x\frac{dy}{dx}}{y^2})$

                                      $=2(\dfrac{y-x(\frac{2x}{y})}{y^2})=\dfrac{2y^2-4x^2}{y^3}$

                                     $=\dfrac{-(4x^2-2y^2))}{y^3}=-\dfrac{9}{y^3} \boxed{\because 4x^2-2y^2=9}$