How do you find the derivative of y in the equation ln(xy)=x+y

rancuri5a

rancuri5a

Answered question

2022-09-06

How do you find the derivative of y in the equation ln ( x y ) = x + y ?

Answer & Explanation

Marshall Horne

Marshall Horne

Beginner2022-09-07Added 8 answers

You have to remember that in this "implicit" function y is a function of x so deriving you get: 1 x y ( y + x d y d x ) = 1 + d y d x where you used the Chain Rule on the ln
Then:
1 x + 1 y d y d x = 1 + d y d x
So you collect d y d x and get:
d y d x = 1 - 1 x 1 y - 1 = ( x - 1 x ) ( y 1 - y ) = y ( x - 1 ) x ( 1 - y )

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