Given that $\sin 2{{x}^{2}}{{y}^{3}}=3{{x}^{3}}+1$, find an expression of \(\frac{\mathrm{d}y

Question

Given that $\sin 2{{x}^{2}}{{y}^{3}}=3{{x}^{3}}+1$, find an expression of $\frac{\mathrm{d}y}{\mathrm{d}x}$.

Accepted Answer

$\frac{9x-4{{y}^{3}}\cos 2{{x}^{2}}{{y}^{3}}}{6x{{y}^{2}}\cos 2{{x}^{2}}{{y}^{3}}}$

Techniques of Differentiation - Implicit Differentiation