Given that $5=4{{x}^{2}}+5{{y}^{2}}$, find an expression of \(\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d

Question

Given that $5=4{{x}^{2}}+5{{y}^{2}}$, find an expression of $\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}$.

Accepted Answer

$\frac{{{\mathrm{d}}^{2}}y}{\mathrm{d}{{x}^{2}}}=\frac{-20{{y}^{2}}-16{{x}^{2}}}{25{{y}^{3}}}$

Applications of Differentiation