Answer:
y' = (y⁴ + 10x) / (y² − 4xy³)
Explanation:
3xy⁴ − y³ + 15x² = 40
Take derivative of both sides with respect to x, using product rule and chain rule:
3(x 4y³ y' + y⁴) − 3y² y' + 30x = 0
Simplify and solve for y':
4xy³ y' + y⁴ − y² y' + 10x = 0
y⁴ + 10x = y² y' − 4xy³ y'
y⁴ + 10x = (y² − 4xy³) y'
y' = (y⁴ + 10x) / (y² − 4xy³)