http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 17:15:18 GMT Wed, 10 Jun 2026 17:15:18 GMT The latest answers and comments added to the Question, MultiVariate Directional Derivative http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78037 Try this: restart; VectorCalculus[DirectionalDiff](x*exp(y)/(3*z^2+1), <1,-2,3>,[x,y,z]); However, if you have several directional derivatives to compute you could do this: restart; f := (a,b,c)->VectorCalculus[DirectionalDiff](x*exp(y)/(3*z^2+1),<a,b,c> ,[x, y, z] ): f(1,-2,3); f(4,-5,6); Hope this helps, J. Tarr Try this: restart; VectorCalculus[DirectionalDiff](x*exp(y)/(3*z^2+1), <1,-2,3>,[x,y,z]); However, if you have several directional derivatives to compute you could do this: restart; f := (a,b,c)->VectorCalculus[DirectionalDiff](x*exp(y)/(3*z^2+1),<a,b,c> ,[x, y, z] ): f(1,-2,3); f(4,-5,6); Hope this helps, J. Tarr 78037 Tue, 27 Feb 2007 01:08:09 Z Mariner Mariner http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78036 Thanks, but all these methods give me functions of x, y, z. I wanted the directional derivative evaluated at a particular point with numerical rectangular coordinates, an answer something like 3 or sqrt(5) or Pi. John Vawter Thanks, but all these methods give me functions of x, y, z. I wanted the directional derivative evaluated at a particular point with numerical rectangular coordinates, an answer something like 3 or sqrt(5) or Pi. John Vawter 78036 Tue, 27 Feb 2007 01:22:20 Z John Vawter John Vawter http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78033 The directional derivative will evaluate to a simple numerical answer if the derivatives of the function are constants. For example: restart; f := (a,b,c)->VectorCalculus[DirectionalDiff](2*x+3*y+4*z+1,<a,b,c> ,[x, y, z] ): f(1,-2,3); f(4,-5,6); Hope this helps, J. Tarr The directional derivative will evaluate to a simple numerical answer if the derivatives of the function are constants. For example: restart; f := (a,b,c)->VectorCalculus[DirectionalDiff](2*x+3*y+4*z+1,<a,b,c> ,[x, y, z] ): f(1,-2,3); f(4,-5,6); Hope this helps, J. Tarr 78033 Tue, 27 Feb 2007 02:50:40 Z Mariner Mariner http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78031 So, a numerical directional derivative for functions of 3 variables is only obtainable with a hyperplane where the gradient is constant? Giving one variable an exponent of 2 in your example function gives me a directional derivative which is a function of that variable. (Of course, a control-click (right click) allows evaluation at any point.) John Vawter So, a numerical directional derivative for functions of 3 variables is only obtainable with a hyperplane where the gradient is constant? Giving one variable an exponent of 2 in your example function gives me a directional derivative which is a function of that variable. (Of course, a control-click (right click) allows evaluation at any point.) John Vawter 78031 Tue, 27 Feb 2007 04:05:54 Z John Vawter John Vawter http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78024 Sorry, I misread your question. The directional derivative can be evaluated at any given point by substituting the value of that point's coordinates in the derivative. For example: restart; with(VectorCalculus): sph := (x-a)^2+(y-b)^2+(z-c)^2-r^2; dd := DirectionalDiff( sph , <v1,v2,v3>, [x,y,z] ); v1,v2,v3 := 1,2,3; dd; x,y,z := 4,5,6; dd; a,b,c := 0,0,0; dd; You can, of course, use eval, or subs, if that is more convenient. J. Tarr Sorry, I misread your question. The directional derivative can be evaluated at any given point by substituting the value of that point's coordinates in the derivative. For example: restart; with(VectorCalculus): sph := (x-a)^2+(y-b)^2+(z-c)^2-r^2; dd := DirectionalDiff( sph , <v1,v2,v3>, [x,y,z] ); v1,v2,v3 := 1,2,3; dd; x,y,z := 4,5,6; dd; a,b,c := 0,0,0; dd; You can, of course, use eval, or subs, if that is more convenient. J. Tarr 78024 Tue, 27 Feb 2007 12:44:51 Z Mariner Mariner http://www.mapleprimes.com/questions/41791-MultiVariate-Directional-Derivative?ref=Feed:MaplePrimes:MultiVariate Directional Derivative:Comments#answer78020 Good work, J. Tarr. That does it. I am curious about the way Maple works here. Once the directional derivative is defined, entering a vector, coordinates or other parameters requires that you call the directional derivative function again and presumably update it. I guess there is no way to call the directional derivative function just once (after you have defined a vector and point)? (I did try this and got an "unknown coordinate system: [4, 5, 6]" error.) Thanks again, John Vawter Good work, J. Tarr. That does it. I am curious about the way Maple works here. Once the directional derivative is defined, entering a vector, coordinates or other parameters requires that you call the directional derivative function again and presumably update it. I guess there is no way to call the directional derivative function just once (after you have defined a vector and point)? (I did try this and got an "unknown coordinate system: [4, 5, 6]" error.) Thanks again, John Vawter 78020 Wed, 28 Feb 2007 10:27:01 Z John Vawter John Vawter