Pregunta: Find all the second order partial derivatives for the following: 1. f(x,y)=x+y+xy 2. f(x,y)=sinxy 3. g(x,y)=x2y+cosy+ysinx

Ans 1 Given Function $\mathrm{f}(\mathrm{x},\mathrm{y})=\mathrm{x}+\mathrm{y}+\mathrm{x}\mathrm{y}$

Now we have to determine the following partial derivative :

$\frac{\partial \mathrm{f}}{\partial \mathrm{x}}=\frac{\partial (\mathrm{x}+\mathrm{y}+\mathrm{x}\mathrm{y})}{\partial \mathrm{x}}=1+\mathrm{y}$ , $\frac{{\partial }^2\mathrm{f}}{\partial {\mathrm{x}}^2}=\frac{\partial (1+\mathrm{y})}{\partial \mathrm{x}}=0$