Help Plotting Mathematica Functions f(x,y) & sin(exp(xy))

[billyd690]

The goal is to plot both the surface graph of the function and the tangent plane to the surface on one plot. There are two functions I believe I'm having issues with:

f(x,y) = cos(x+y)exp(x^2 - y^2) @ point (0.5,-0.5)

&

f(x,y) = sin(exp(xy)) @ point (1,1)

My code for the two are as follows respectively:

Clear[f,x,y,fx,fy,point1,point2]
point1=0.5;
point2=-0.5;
f[x_,y_]=cos(x+y)exp((x^2) - (y^2));
fx[x_,y_]=D[f[x,y],x];
fy[x_,y_]=D[f[x,y],y];
T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)
T[x,y]

Clear[G1,G2];
G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]
G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]
Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

for the second:

Clear[f,x,y,fx,fy,point1,point2]
point1=1;
point2=1;
f[x_,y_]= sin(exp(xy));
fx[x_,y_]=D[f[x,y],x];
fy[x_,y_]=D[f[x,y],y];
T[x_,y_]:=f[point1,point2]+fx[point1,point2](x-point1)+fy[point1,point2](y-point2)
T[x,y]

Clear[G1,G2];
G1=Plot3D[f[x,y],{x,-2,10},{y,-4,4}]
G2=Plot3D[T[x,y],{x,-2,10},{y,-4,4}]
Show[G1,G2,ViewPoint -> {0,-2,0.3},AspectRatio -> 1,AxesLabel -> {"x","y","f(x,y)"}]

I believe the outputs I'm getting are wrong. For the cos one it just plots a flat plane at 0. For the second one there isn't any plot. I've changed around the intervals and viewpoints, but still nothing shows up. Just looking for a little insight into the issue. thanks!

 

[Bill Simpson]

Change all the following

sin(x) to Sin[x]
cos(x) to Cos[x]
exp(x) to Exp[x]
xy to x*y
f[x_,y_]= to f[x_,y_]:= except for f[x_,y_]=D[], those need =
but you need to carefully check use of = versu := to make certain your functions are behaving exactly as you need
and separate each of your "statements" with semicolons.

Look at the scale of your G1 and G2 plots, One of those seems to range over -5*10^15 to 5*10^15 while the other ranges over -5 to 15 and I suspect that is a problem.

That should get you started. When you have all those fixed post an update showing what you have.

Mathematica is FANATIC about correct use of [] versus () versus {} and correct capitalization and correct use of = versus := versus == and there is even an === and those are all completely different. Make any tiny mistake with anyone of those and you will get incorrect results or error messages you may not understand or even nothing at all.

 

[billyd690]

Thank you for that! I am new to using Mathematica and didn't realize it was so case sensitive and such. I knew it was something but I wasn't sure because I didn't receive any error messages. I've got it know and have actual graphs now.

Thanks again.