$3y\left(3x^2+y^2\right)^2$  

 $3x^2\left(3x^2+y^2\right)^2$  

 $6\left(3x^2+y^2\right)^2$  

 $6y\left(3x^2+y^2\right)^2$  

 $8xy+3$  

 $8xy-5$  

 $4x^2+3$  

 $4x^2+3y$  

$f_{xy}=f_{xx}$

$f_{xy}=f_{yx}$

$f_{xx}=f_{yy}$

$f_{xy}=f_{yy}$

 $f_x=3x^2-2y+y^3;\ f_y=6x$  

 $f_{xx}=6x;\ f_{xy}=-2+3y^2$  

 $f_x=-2x+6y+3xy^2;$   $f_y=3x^2-2y+y^3$  

 $f_{xx}=6+6xy;f_{yy}=6x$  

 $3y\left(3x^2+y^2\right)^2$  

 $3x^2\left(3x^2+y^2\right)^2$  

 $6\left(3x^2+y^2\right)^2$  

 $6y\left(3x^2+y^2\right)^2$  

 $f_{yy}(x,y)=24(3x+2y)^2$  
 $f_{xx}(x,y)=12(3x+2y)^2\ ,\$  

 $f_{yy}(x,y)=8(3x+2y)^3$ 
  $f_{xx}(x,y)=36(3x+2y)^2,$  

 $f_{xy}(x,y)=32(3x+2y)$  
 $f_{xx}(x,y)=24(3x+2y)^2,\$  

 $f_{xx}(x,y)=108(3x+2y)^2,\$   $f_{yy}(x,y)=48(3x+2y)^2$  

 $f_x(x,y)=3x^2-2y+y^3$   $f_y(x,y)=-2x+6y+3xy^2$   $f_{xy}(x,y)=6x$  

 $f_x(x,y)=-2x+6y+3xy^2$   $f_y(x,y)=3x^2-2y+y^3$   $f_{xy}(x,y)=-2+3y^2$  

 $f_{xx}(x,y)=6x$   $f_{yy}(x,y)=6+6xy$  
 $f_{xy}(x,y)=-2+3y^2$  

 $f_{xx}(x,y)=6+6xy$   $f_{yy}(x,y)=6x$  
 $f_{xy}(x,y)=-2+3y^2$  

 $dz=\left(2x-5y\right)dx+5xdy$  

 $dz=\left(2x-5y\right)dx-5xdy$  

 $dz=\left(2x-5y\right)\partial x+5x\partial y$  

 $dz=\left(2x-5y\right)\partial x-5x\partial y$  

 $dz=\frac{\partial x}{\partial y}dx+\frac{\partial x}{\partial y}dy$  

 $dz=\frac{\partial z}{\partial x}dx+\frac{\partial z}{\partial y}dy$  

 $dz=\frac{\partial z}{\partial x}dy+\frac{\partial z}{\partial y}dx$  

 $dz=\frac{\partial z}{\partial x}\frac{\text{d}x}{\text{d}y}+\frac{\partial z}{\partial y}\frac{\text{d}x}{\text{d}y}$