Derivative at its Peak.

Calculus Level 4

$R=\dfrac{\left[1+\left( \dfrac{dy}{dx}\right)^2 \right]^{\frac{3}{2}}}{\dfrac{d^2y}{dx^2}}$ , then $$R^{\frac{2}{3}}$$ can be put in the form of :

$A. \frac{1}{\left(\frac{d^2y}{dx^2}\right)^{\frac{2}{3}}}+\frac{1}{\left(\frac{d^2x}{dy^2}\right)^{\frac{2}{3}}}$ $B.\frac{1}{\left(\frac{d^2y}{dx^2}\right)^{\frac{3}{2}}}+\frac{1}{\left(\frac{d^2x}{dy^2}\right)^{\frac{3}{2}}}$ $C. \frac{2}{\left(\frac{d^2y}{dx^2}\right)^{\frac{2}{3}}}+\frac{2}{\left(\frac{d^2x}{dy^2}\right)^{\frac{2}{3}}}$ $D.\frac{1}{\left(\frac{d^2y}{dx^2}\right)^{\frac{2}{3}}} \cdot \frac{1}{\left(\frac{d^2x}{dy^2}\right)^{\frac{2}{3}}}$ Choose the right option.

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