Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

Techniques of Differentiation - Higher Derivatives by Implicit Differentiation

Given that \(4{{y}^{2}}+2=3{{x}^{2}}\), find an expression of \(\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}\).

Solution:

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Answer:\(\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac3{8y^3}\), for \(y\ne0\).

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