Techniques of Differentiation - Higher Derivatives by Implicit Differentiation
Techniques of Differentiation - Higher Derivatives by Implicit Differentiation
Given that \(5=4{{x}^{2}}+5{{y}^{2}}\), find an expression of \(\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}\).
Solution:
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Answer:\(\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac4{5y^3}=\dfrac{-20y^2-16x^2}{25y^3}\), on either branch with \(y\ne0\).
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