Exercise
$\frac{d}{dx}\left(\frac{x^3y-3xy^2}{4x^4-5xy^2}=0\right)$
Step-by-step Solution
Final answer to the exercise
$\sqrt[3]{3x^{2}y+x^3y^{\prime}+3\left(-y^2-2xy\cdot y^{\prime}\right)}\sqrt[3]{4x^4-5xy^2}+\sqrt[3]{-x^3y+3xy^2}\sqrt[3]{16x^{3}+5\left(-y^2-2xy\cdot y^{\prime}\right)}=0,\:\sqrt[3]{\left(3x^{2}y+x^3y^{\prime}+3\left(-y^2-2xy\cdot y^{\prime}\right)\right)^{2}}\sqrt[3]{\left(4x^4-5xy^2\right)^{2}}-\sqrt[3]{3x^{2}y+x^3y^{\prime}+3\left(-y^2-2xy\cdot y^{\prime}\right)}\sqrt[3]{4x^4-5xy^2}\sqrt[3]{-x^3y+3xy^2}\sqrt[3]{16x^{3}+5\left(-y^2-2xy\cdot y^{\prime}\right)}+\sqrt[3]{\left(-x^3y+3xy^2\right)^{2}}\sqrt[3]{\left(16x^{3}-5\left(y^2+2xy\cdot y^{\prime}\right)\right)^{2}}=0$