Calculus  Verify?
posted by Aric on .
Find the slope of the tangent line to the curve (a lemniscate)
2(x^2+y^2)^2 = 25(x^2y^2)
it is at pt (3,1)

:4(x² + y²)(2x + 2y dy/dx) = 25(2x  2y dy/dx).
:4[(3)² + (1)²][2(3) + 2(1)dy/dx] = 25[2(3)  2(1)dy/dx]
:4[9 + (1)][6 + 2 dy/dx] = 25[6  2 dy/dx]
:4[10][8 dy/dx] = 25[4 dy/dx]
Divide both sides by 10
:4[8 dy/dx] = 10[dy/dx]
:32[dy/dx] = 10 [dy/dx]
then I got dy/dx = 10/32 
You messed up near the end
look at line
4[9 + (1)][6 + 2 dy/dx] = 25[6  2 dy/dx]
and then
4[10][8 dy/dx] = 25[4 dy/dx]
you added "unlike terms" inside the bracket
should have been
40[6+2dy/dx] = 25[62dy/dx]
240 + 80dy/dx = 150  50dy/dx
130dy/dx = 90
dy/dx = 90/130 = 9/13
the rest is easy. 
tyvm <3