Derivative at its Peak.

Calculus Level 5

R=[1+(dydx)2]32d2ydx2R=\dfrac{\left[1+\left( \dfrac{dy}{dx}\right)^2 \right]^{\frac{3}{2}}}{\dfrac{d^2y}{dx^2}} , then R23R^{\frac{2}{3}} can be put in the form of :

A.1(d2ydx2)23+1(d2xdy2)23A. \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.1(d2ydx2)32+1(d2xdy2)32B.\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.2(d2ydx2)23+2(d2xdy2)23C. \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.1(d2ydx2)231(d2xdy2)23D.\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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