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3 years ago

3xy^4-y^3+15x^2=40 Find y’

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Answer:

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)

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