Given that $5{{x}^{3}}+x{{y}^{2}}=5{{x}^{3}}{{y}^{3}}$, find an expression of \(\frac{{\mathr

Question

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

Accepted Answer

$\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{15{{x}^{2}}{{y}^{3}}-15{{x}^{2}}-{{y}^{2}}}{2xy-15{{x}^{3}}{{y}^{2}}}$

Techniques of Differentiation - Implicit Differentiation