How to find dy/dx by implicit differentiation given xy^3=y+x?

Aiyana Jenkins

Aiyana Jenkins

Answered question

2023-03-06

How to find d y d x by implicit differentiation given x y 3 = y + x ?

Answer & Explanation

sayko11czj

sayko11czj

Beginner2023-03-07Added 2 answers

On both sides, differentiate each term implicitly with respect to x
Note differentiate x y 3 using product rule
( x .3 y 2 . d y d x + y 3 .1 ) = d y d x + 1
3 x y 2 d y d x - d y d x = 1 - y 3
d y d x ( 3 x y 2 - 1 ) = 1 - y 3
d y d x = 1 - y 3 3 x y 2 - 1

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