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So I'm trying to make a mathematica program that let's me manipulate the components and position of a directional vector and show the value of the directional derivative. Right now I'm still trying to get it to let me manipulate a directional vector on a plot. I tried to get the directional vector on the plot using

Show[{coolthing, Graphics3D[ Arrow[{Manipulate[{x, y, 2 x^2 + 2 y^2}, {x, -10, 10}, {y, -10, 10}]}, {Manipulate[{a, b, c}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}]}]]}]

coolthing is the plot of the function $f(x,y)=x^{2}+y^{2}$. Apparently Mathematica isn't cool with me entering the coordinates the arrow goes from and to as manipulatable variables though. Is there a way to get to get it to accept the manipulate command for these coordinates? I've tried wrapping the manipulate command around different parts of the code but nothing seems to be working.

So I'm trying to make a mathematica program that let's me manipulate the components and position of a directional vector and show the value of the directional derivative. Right now I'm still trying to get it to let me manipulate a directional vector on a plot. I tried to get the directional vector on the plot using

Show[{coolthing, Graphics3D[ Arrow[{Manipulate[{x, Arrow[Manipulate[{x, y, 2 x^2 + 2 y^2}, {x, -10, 10}, {y, -10, 10}]}, {Manipulate[{a, 10}], Manipulate[{a, b, c}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}, {c, -10, 10}]}]]}]10}]]]}]

coolthing is the plot of the function $f(x,y)=x^{2}+y^{2}$. Apparently Mathematica isn't cool with me entering the coordinates the arrow goes from and to as manipulatable variables though. Is there a way to get to get it to accept the manipulate command for these coordinates? I've tried wrapping the manipulate command around different parts of the code but nothing seems to be working.

So I'm trying to make a mathematica program that let's me manipulate the components and position of a directional vector and show the value of the directional derivative. Right now I'm still trying to get it to let me manipulate a directional vector on a plot. I tried to get the directional vector on the plot using

Show[{coolthing, Graphics3D[ Arrow[Manipulate[{x, y, 2 x^2 + 2 y^2}, {x, -10, 10}, {y, -10, 10}], Manipulate[{a, b, c}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}]]]}]

coolthing is the plot of the function $f(x,y)=x^{2}+y^{2}$. Apparently Mathematica isn't cool with me entering the coordinates the arrow goes from and to as manipulatable variables though. Is there a way to get to get it to accept the manipulate command for these coordinates? I've tried wrapping the manipulate command around different parts of the code but nothing seems to be working.

So I'm trying to make a mathematica program that let's me manipulate the components and position of a directional vector and show the value of the directional derivative. Right now I'm still trying to get it to let me manipulate a directional vector on a plot. I tried to get the directional vector on the plot using

Show[{coolthing, Graphics3D[ Arrow[Manipulate[{x, Show[Plot3D[ x + y, x^2 {x, -10, 10}, {y, -10, 10}, ColorFunction -> "Rainbow", Mesh -> None],

Manipulate[ Graphics3D[Arrow[{{u, v, u + y^2}, v}, {a, b, c}}]], {u, -10, 10}, {v, -10, 10}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}],

PlotRange -> All, AxesLabel -> {x, -10, 10}, {y, -10, 10}], Manipulate[{a, b, c}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}]]]}]

coolthing y, z}, ImageSize -> {400, 400}]

Mathematica is the plot of the function $f(x,y)=x^{2}+y^{2}$. Apparently Mathematica isn't cool fine with me entering the coordinates the arrow goes from both of the graphics separately but when I use the Show command to put them in the same image I get an error message that says one of my options was not formatted as a rule and to as manipulatable variables though. Is there a way to get to get it to accept the manipulate command for that skeleton is not a graphics3D primitive or derivative. Does anyone know what these coordinates? I've tried wrapping the manipulate command around different parts of the code but nothing seems to be working.messages are trying to tell me?

So I'm trying to make a mathematica program that let's me manipulate the components and position of a directional vector and show the value of the directional derivative. Right now I'm still trying to get it to let me manipulate a directional vector on a plot. I tried to get the directional vector on the plot using

Show[Plot3D[ x + y, {x, -10, 10}, {y, -10, 10}, ColorFunction -> "Rainbow", Mesh -> None],

Manipulate[ Graphics3D[Arrow[{{u, v, u + v}, {a, b, c}}]], {u, -10, 10}, {v, -10, 10}, {a, -10, 10}, {b, -10, 10}, {c, -10, 10}],

PlotRange -> All, AxesLabel -> {x, y, z}, ImageSize -> {400, 400}]

Mathematica is fine with both of the graphics separately but when I use the Show command to put them in the same image I get an error message that says one of my options was not formatted as a rule and that skeleton is not a graphics3D primitive or derivative. Does anyone know what these messages are trying to tell me?