Partial Derivatives
Section 14.2
#5, 15, 24 -- p. 936
Andy Long, Fall, 2015

f[x_,y_]:=-Sin[y]x^2
Plot3D[f[x,y],{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]

fsubx=D[f[x,y],x]
fsuby=D[f[x,y],y]
Plot3D[fsubx,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]
Plot3D[fsuby,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]

#15

f[x_,y_]:=y^5-3x y
Plot3D[f[x,y],{x,-Pi,Pi},{y,-Pi,Pi},AxesLabel->Automatic]

fsubx=D[f[x,y],x]
fsuby=D[f[x,y],y]
Plot3D[fsubx,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]
Plot3D[fsuby,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]

#15

f[x_,y_]:=E^y/(x+y^2)
Plot3D[f[x,y],{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]

fsubx=D[f[x,y],x]
fsuby=D[f[x,y],y]
Plot3D[fsubx,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]
Plot3D[fsuby,{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->30,AxesLabel->Automatic]