Find the value of frac{d^2x}{dy^2}. | vedclass

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(D) We know that $\frac{dx}{dy} = \frac{1}{dy/dx}$.Now,differentiating both sides with respect to $y$:$\frac{d^2x}{dy^2} = \frac{d}{dy} \left( \frac{1

Vedclass · Accepted Answer

$\frac{-(d^2y/dx^2)}{(dy/dx)^3}$

Vedclass · Answer

(D) We know that $\frac{dx}{dy} = \frac{1}{dy/dx}$.Now,differentiating both sides with respect to $y$:$\frac{d^2x}{dy^2} = \frac{d}{dy} \left( \frac{1}{dy/dx} \right)$.Using the chain rule,$\frac{d}{dy} = \frac{dx}{dy} \cdot \frac{d}{dx} = \frac{1}{dy/dx} \cdot \frac{d}{dx}$.Therefore,$\frac{d^2x}{dy^2} = \frac{1}{dy/dx} \cdot \frac{d}{dx} \left( (dy/dx)^{-1} \right)$.$= \frac{1}{dy/dx} \cdot \left( -1 \cdot (dy/dx)^{-2} \cdot \frac{d^2y}{dx^2} \right)$.$= -\frac{d^2y/dx^2}{(dy/dx)^3}$.

Find the value of $\frac{d^2x}{dy^2}$.

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