How to differentiate xy^2-x^3y=6?

ngukusizabw7

ngukusizabw7

Answered question

2023-02-13

How to differentiate x y 2 - x 3 y = 6 ?

Answer & Explanation

Leticia Robertson

Leticia Robertson

Beginner2023-02-14Added 8 answers

You use an Implicit Function in which y is function of x so you have to derive it as well.
You get:
( 1 y 2 + 2 x y d y d x ) - ( 3 x 2 y + x 3 d y d x ) = 0 using the Product Rule.
Then:
y 2 + 2 x y d y d x - 3 x 2 y - x 3 d y d x = 0
Collecting d y d x :
d y d x [ 2 x y - x 3 ] = 3 x 2 y - y 2
d y d x = y ( 3 x 2 - y ) x ( 2 y - x 2 )

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