How to implicitly differentiate -y= x^3y^2-3x^2y^3-7xy^4?

Darren Salas

Darren Salas

Answered question

2023-02-18

How to implicitly differentiate - y = x 3 y 2 - 3 x 2 y 3 - 7 x y 4 ?

Answer & Explanation

Talon Mcfarland

Talon Mcfarland

Beginner2023-02-19Added 9 answers

- y = x 3 y 2 - 3 x 2 y 3 - 7 x y 4
Using the chain and product rules, proceed now ...
- y = 3 x 2 y 2 + x 3 ( 2 y y ) - 6 x y 3 - 3 x 2 ( 3 y 2 y ) - 7 y 4 - 7 x ( 4 y 3 y )
Next combine the y terms on the left side of the equation ...
y [ - 1 - x 3 ( 2 y ) + 3 x 2 ( 3 y 2 ) + 7 x ( 4 y 3 ) ] = 3 x 2 y 2 - 6 x y 3 - 7 y 4
Finally, simplify and solve for y
y = 3 x 2 y 2 - 6 x y 3 - 7 y 4 9 x 2 ( y 2 ) + 28 x ( y 3 ) - x 3 ( 2 y ) - 1

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