hello.

find derivative of:

y = ln(5x² + y²)

Using method described at:

Solutions to Implicit Differentiation Problems
I get:

y' = D{ln(5x² + y²)}

y' = 1/(5x² + y²) D{(5x² + y²)}

y' = 1/(5x² + y²) (10x + 2y y')

y' = 10x/(5x² + y²) + 2y y'/(5x² + y²)

y' - 2y y'/(5x² + y²) = 10x/(5x² + y²)

y'(5x² + y²)/(5x² + y²) - 2y y'/(5x² + y²) = 10x/(5x² + y²)

(y'(5x² + y²) - 2y y')/(5x² + y²) = 10x/(5x² + y²)

y'(5x² + y² - 2y)/(5x² + y²) = 10x/(5x² + y²)

y' = 10x/(5x² + y²) (5x² + y²)/(5x² + y² - 2y)

y' = 10x/(5x² + y² - 2y)

I like to use online tools to check my work. There are several that purport to solve this type of equation. They all seem to agree that the answer is:

y' = 10x/(5x² + y²)

Of course, they don't show steps, so I can't tell if I'm just wrong or if the online tools are wrong (or if I'm using them wrong).

Where's the error?