Homework 14.3
MAT329
Andy Long, Fall, 2015

#5: I’ve created a model for the function. You don’t need to do this, but I encourage it!

f[x_,y_]:=(2x)^2*Sin[y]
Plot3D[f[x,y],{x,-3,3},{y,-3,3},AxesLabel->Automatic,BoxRatios->{1,1,1.2}]
fx[x_,y_]=D[f[x,y],x]
fy[x_,y_]=D[f[x,y],y]
N[fx[1,2]]
N[fy[1,2]]

#63: you can do it all at once,

f[x_,y_]:=x^4y^2-x^3y
D[f[x,y],{x,3}]
D[f[x,y],x,y,x]

or more slowly:

Clear[fx,fy,fxx,fxy,fyy,fxxx,fxyx]
fx[x_,y_]=D[f[x,y],x]
fy[x_,y_]=D[f[x,y],y]
fxx[x_,y_]=D[fx[x,y],x]
fxy[x_,y_]=D[fx[x,y],y]
fxxx[x_,y_]=D[fxx[x,y],x]
fxyx[x_,y_]=D[fxy[x,y],x]