restart:

f := x1^2/(x2^3*x3^2*x4*x5^10);

n := 5;

x := seq(eval(cat('x', i)), i = 1 .. n);

for i from 2 to n do

op(1, op(i, f))^sign(op(2, op(i, f)))

                                                      end do;

@Hypnos 

restart: with(RootFinding):

f1 := c1+2*c2-3:

f2 := c1+9*c2-5:

f3 := c1^2+c2^2-1:

solve({f1, f2, f3}, {c1, c2});

Isolate([f1, f2, f3], [c1, c2]);

“Solve” is nothing  and  “Isolate”  is  empty... Maple15

“nothing return after solve({y1 = c1*x1 + c2*x2, y2 = c1*x3 + c2*x4, c1^2 + c2^2 = 1}, {c1,c2});”

How many variables (n) and how many equations (m)? It is necessary that n = m  

restart;

f := ln(x);

(diff(f, x))/(diff(ln(x), x));

1;

@Markiyan Hirnyk  ?

http://hostingkartinok.com/show-image.php?id=de847a09264bc43e9ad728995cfeeb59

http://hostingkartinok.com/show-image.php?id=09dcc30c0406a759d0b4e9a9d314e6a4

That was my mistake.

Draghilev.

Small remark: Diaghilev. Draghilev A.V. requested the so to write his name in English.

@Kitonum 

Shall look for more examples...

(x1+0.7e-1*sin(30*x2)^2)^2+(x2+0.7e-1*sin(30*x1)^2)^2-1=0;

http://radikale.ru/data/upload/c2184/0fccf/c7cd7bb962.gif

(It is moving perpendicular and tangent to each point.)

Theta has a period of (2n+-1)* Pi, and x has a period of (2n+-1)* Pi

Theta has a period of (2n+-1)* Pi, and x has a period of (2n+-1)* Pi

restart;

 f := Z^6-3*Z^4+3*Z^2+Z-1;

for i to 6 do op(i, [evalf(solve(f))]) end do;

restart;

 f := Z^6-3*Z^4+3*Z^2+Z-1;

for i to 6 do op(i, [evalf(solve(f))]) end do;