How do you use implicit differentiation to find \(\frac{dy}{dx}\) for the equation \(x^2 + 3xy + y^3 = 10\)?

x 2 + 3 x y + y 3 = 10 2 x + 3 x y ′ + 3 y + 2 y y ′ = 0 ( 2 x + 3 y ) + ( 3 x y ′ + 2 y y ′ ) = 0 2 x + 3 y + ( 3 x + 2 y ) y ′ = 0 ( 3 x + 2 y ) y ′ = − 2 x − 3 y / : ( 3 x + 2 y ) y ′ = 3 x + 2 y − 2 x − 3 y ​

Answered by vivindalka | 2024-06-10

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Answered by IamONLYgoodFORmath | 2024-06-12

To find d x d y ​ for the equation x 2 + 3 x y + y 3 = 10 , first differentiate both sides implicitly. After applying the rules of differentiation and rearranging, the result is d x d y ​ = 3 ( x + y 2 ) − 2 x − 3 y ​ .
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Answered by vivindalka | 2024-12-20