3xy^4-y^3+15x^2=40

Find y'

y' = (y⁴ + 10x) / (y² - 4xy³)

Step-by-step 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)