1
$\begingroup$

I am given a system $$\left\{\begin{matrix}xy^2+zu+v^2=3 \\ x^3z+2y-uv=2 \\ xu+yv-xyz=1 \end{matrix}\right.$$ which defines x, y, z as functions of (u,v) around (1, 1, 1, 1, 1). I've been asked to compute $$\frac{\partial y}{\partial u}(1, 1)$$ and $$\frac{\partial z}{\partial v}(1, 1)$$

I've been struggling to understand how to use the implicitdiff command in Maple. I have looked on Maple Help but I am still confused about how to identify my parameters. If anyone can offer some clarification/tips, that would be greatly appreciated!

$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

Let 

eqs:= {x*y^2 + z*u + v^2=3,x^3*z+2*y-u*v=2,x*u + y*v - x*y*z = 1};

For $\partial y/\partial u$, you would use

implicitdiff(eqs, {x,y,z},y,u);

and then of course you can evaluate this at $(x,y,z,u,v) = (1,1,1,1,1)$:

eval(%, {x=1,y=1,z=1,u=1,v=1});
$\endgroup$
2
  • $\begingroup$ Would the other implicit differentiation be: implicitdiff(eqs, {x, y, z}, z, v)? I've tried putting this in but it returns a 'fail'. I'm not sure what I've entered in wrong. $\endgroup$
    – grizzly.bear
    Apr 7, 2016 at 22:58
  • $\begingroup$ For implicitdiff(eqs, {x, y, z}, z, v), I get $${\frac {-6\,{x}^{3}{z}^{2}v-6\,{y}^{2}{x}^{3}z+{y}^{2}xzu+6\,{x}^{2}z{ v}^{2}-2\,yx{u}^{2}+{y}^{2}uv+4\,yzv+2\,{y}^{3}-4\,uv}{-5\,{y}^{2}{x}^ {4}z-2\,y{x}^{4}u+3\,{x}^{3}{z}^{2}u+{y}^{2}{x}^{3}v-3\,{x}^{2}zuv+2\, {y}^{3}x-2\,yzu+2\,{u}^{2}}} $$ I don't know where your "fail" is coming from. Maybe a typo somewhere. $\endgroup$
    – Robert Israel
    Apr 8, 2016 at 15:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.