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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!

grizzly.bear
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1 Answers1

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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});
Robert Israel
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  • 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. – grizzly.bear Apr 07 '16 at 22:58
  • 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. – Robert Israel Apr 08 '16 at 15:51