2x − 16y + (2y − 16x)(dy/dx) = 0. Solve for dy/dx.
To solve for dy/dx, we can first simplify the equation:
2x - 16y + (2y - 16x)(dy/dx) = 0
Distribute (dy/dx) to (2y - 16x):
2x - 16y + 2y(dy/dx) - 16x(dy/dx) = 0
Rearrange the terms:
2x - 16x(dy/dx) - 16y + 2y(dy/dx) = 0
Combine like terms:
(2x - 16x(dy/dx)) + (2y(dy/dx) - 16y) = 0
Factor out (dy/dx):
(2x - 16x) + (2y - 16y)(dy/dx) = 0
Simplify:
-14x - 14y(dy/dx) = 0
Divide both sides by -14x and -14y:
(dy/dx) = 0/(-14x) + 0/(-14y)
(dy/dx) = 0 + 0
dy/dx = 0
Therefore, the solution for dy/dx is 0.