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12 April, 11:40
3xy^4-y^3+15x^2=40
Find y'
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Keyon Fletcher
12 April, 14:39
0
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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