Question Number 88179 by ubaydulla last updated on 08/Apr/20
$${z}={x}^{\mathrm{2}} /{y}^{\mathrm{3}} \:\:\:\:\:\:\:\:\:\:{dz}=? \\ $$
Answered by TANMAY PANACEA. last updated on 08/Apr/20
$${dz}=\left(\frac{\partial{z}}{\partial{x}}\right)_{{y}} {dx}+\left(\frac{\partial{z}}{\partial{y}}\right)_{{x}} {dy} \\ $$$$=\frac{\mathrm{1}}{{y}^{\mathrm{3}} }×\mathrm{2}{xdx}+{x}^{\mathrm{2}} ×\left(−\mathrm{3}\right){y}^{−\mathrm{4}} {dy} \\ $$$${dz}=\frac{\mathrm{2}{xdx}}{{y}^{\mathrm{3}} }−\frac{\mathrm{3}{x}^{\mathrm{2}} {dy}}{{y}^{\mathrm{4}} } \\ $$