Given that ${{x}^{4}}+6x{{y}^{2}}+5{{y}^{3}}=0$, find an expression of \(\frac{{\mathrm{d}y}}

Question

Given that ${{x}^{4}}+6x{{y}^{2}}+5{{y}^{3}}=0$, find an expression of $\frac{{\mathrm{d}y}}{\mathrm{d}x}$.

Accepted Answer

$\frac{-4{{x}^{3}}-6{{y}^{2}}}{12xy+15{{y}^{2}}}$

Techniques of Differentiation - Implicit Differentiation