Question

If 2xy^4 = x^3 + 3xy^2, find dx/dy.

Answer 1

2root2 y - root3

Explanation:

To find dx/dy, x needs to be the subject of formula.

`2x y{}^(4) = x {}^(3) + 3xy {}^(2) \\ 2xy {}^(4) - x {}^(3) - 3xy {}^(2) = 0 \\ x(2y {}^(4) - x {}^(2) - 3y {}^(2) ) = 0 \\ 2y {}^(4) - x {}^(2) - 3y {}^(2) = 0 \\ x {}^(2) = 2y {}^(4) - 3y {}^(2) \\ x = \sqrt{2y {}^(4) - 3y {}^(2) \: \: } = √(2) \: y {}^(2) - √(3) \: y \\ (dx)/(dy) = 2 √(2) \: y - √(3)`