Question Number 184735 by mustafazaheen last updated on 11/Jan/23
$$ \\ $$$${f}\left({x},{y}\right)=\left(\sqrt{\mathrm{3}{xy}^{\mathrm{2}} }\right)\left(\sqrt[{\mathrm{5}}]{{x}^{\mathrm{5}} {y}^{\mathrm{2}} }\right) \\ $$$${f}^{'} \left({x},{y}\right)=?\:\:\:\:\:{f}''\left({x},{y}\right)=? \\ $$$$ \\ $$
Commented by mr W last updated on 11/Jan/23
$${there}\:{are}\:{no}\:{things}\:{like}\:{f}'\left({x},{y}\right)\:{or} \\ $$$${f}''\left({x},{y}\right).\:{if}\:{you}\:{mean}\:\frac{\partial{f}\left({x},{y}\right)}{\partial{x}}\:{or} \\ $$$$\frac{\partial^{\mathrm{2}} {f}\left({x},{y}\right)}{\partial{x}^{\mathrm{2}} },\:{you}\:{should}\:{also}\:{correctly} \\ $$$${write}\:{what}\:{you}\:{want}\:{to}\:{ask}. \\ $$
Commented by mustafazaheen last updated on 11/Jan/23
$${Mr}\:\:\:\:\frac{\partial^{\mathrm{2}} {f}\left({x},{y}\right)}{\partial{x}^{\mathrm{2}} }=? \\ $$
Commented by mr W last updated on 11/Jan/23
$${f}\left({x},{y}\right)=\sqrt{\mathrm{3}}{x}^{\frac{\mathrm{3}}{\mathrm{2}}} {y}^{\frac{\mathrm{7}}{\mathrm{5}}} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{2}}{x}^{\frac{\mathrm{1}}{\mathrm{2}}} {y}^{\frac{\mathrm{7}}{\mathrm{5}}} \\ $$$$\frac{\partial^{\mathrm{2}} {f}}{\partial{x}^{\mathrm{2}} }=\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{4}}{x}^{−\frac{\mathrm{1}}{\mathrm{2}}} {y}^{\frac{\mathrm{7}}{\mathrm{5}}} \\ $$