Question: Find \(\frac{dy}{dx}\) from the implicit function, \(x^{3}+y^{3}-1=0\)

now, \(\frac{d}{dx}(x^{3}+y^{3})=\frac{d}{dx}(1)\)

\(\frac{d}{dx}(x^{3})\)+ \(\frac{d}{dx}(y^{3})= 0\)

\(3x^{2}+3y^{2} \frac{d}{dx}=0\)

\(3y^{2}\frac{d}{dx}= – 3x^{2}\)

\(\frac{d}{dx}\)\(=\)\(-\)\(\frac{x^{2}}{y^{2}}\)