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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