To find total derivative of a any given function in form of f(x,y,z)  , should I simply take the Jacobian of the function? If so, why does that yield a total derivative. As i understand, the total derivative is given in form of df = (df/dx)dx + (df/dy)dy which is not the same as Jf = [(df/dx1)   (df/dx2)  ....   (df/dxn)]

My example here is h(x,y,z) = (x + y - z, sin(xyz) + e )

thx for any help

Is there any command to find an tangent for a fuction in maple. My example here is f(x,y) = x- x - y + y and graphing the function and it's tangent at plane (1,1).

Recently, Robert I helped me with a question: To approximate f(x,y) = y/ xby a polynomial of degree 6 in x -1 and y + 1. He said answer to this is achieved by following: mtaylor (y / x, [x=1,y=-1],7);         If this is correct, what does the 7 do?

2 question

one, how do you plot two graphs together of f(x,y)= x - x - y + y and it's tanget at plane (1,1). i can do it individually but is it just simple as putting them in one notation in plot command?  for f(x,y) i used plot3d(f(x,y)) from -pi to pi for both x and y but don't know how to put tangent in at plane (1,1)

two, how apporoximate f(x,y) = y / x by a polynomial of degree 6 in x-1 and y+1.

any hints or examples  are much appreciated.

thx

How to find the total derivative of h(x,y,z) = (x+ y - z, sin(xyz) + e).

maple help shows partial derivative explanation but has not much for total derivative. I haven't learned total derivatives yet so any help is thankful.

thx

How do i find a nonzero value of C so the function u(x,t) = c(e + e)  satisfies the equation  (du/dt)+u(du/dx)+(du/dx) = 0

I've tried with maple help but seems like i'm getting no where with this.

Any suggestion or help with this is much appreciated.