Question Number 73274 by peter frank last updated on 09/Nov/19
Commented by kaivan.ahmadi last updated on 09/Nov/19
$${t}=\mathrm{0}\Rightarrow{x}=\mathrm{1}\:,\:{y}=\mathrm{0}\Rightarrow \\ $$$$\frac{\partial{f}}{\partial{t}}=\frac{\partial{f}}{\partial{x}}×\frac{\partial{x}}{\partial{t}}+\frac{\partial{f}}{\partial{y}}×\frac{\partial{y}}{\partial{t}}= \\ $$$$\left({siny}+{e}^{{x}} {cosy}\right)\left(\mathrm{2}{t}\right)+\left({xcosy}−{e}^{{x}} {siny}\right)\left(\mathrm{2}{t}\right)\mid_{{t}=\mathrm{0}} = \\ $$$${e}×\mathrm{0}+\left(\mathrm{1}−\mathrm{0}\right)\left(\mathrm{0}\right)=\mathrm{0} \\ $$
Commented by peter frank last updated on 09/Nov/19
$${thank}\:{you} \\ $$