Question Number 140363 by cesarL last updated on 06/May/21
$${My}\:{friends}\:{can}\:{you}\:{help}\:{me}? \\ $$$${f}\left({x},{y}\right)={x}^{\mathrm{3}} {y}^{\mathrm{7}} −\mathrm{4}{e}^{{x}−{y}} \\ $$$${Find}: \\ $$$$\left.{a}\right)\:\frac{\partial^{\mathrm{2}} {f}}{\partial{x}\partial{y}}=? \\ $$$$\left.{b}\right)\:\frac{\partial^{\mathrm{2}} {f}^{\mathrm{2}} }{\partial{y}\partial{x}}=? \\ $$$${Please} \\ $$$$ \\ $$$$ \\ $$
Answered by Dwaipayan Shikari last updated on 06/May/21
$$\frac{\partial}{\partial{x}}.\frac{\partial}{\partial{y}}\left({x}^{\mathrm{3}} {y}^{\mathrm{7}} −\mathrm{4}{e}^{{x}−{y}} \right) \\ $$$$=\mathrm{21}{x}^{\mathrm{2}} {y}^{\mathrm{6}} +\mathrm{4}{e}^{{x}−{y}} \\ $$