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?