Find y' if
y = ln(5x^2 + 9y^2).
use the chain rule
y' = 1/(5x^2 + 9y^2) * (10x + 18yy')
y' (1 - 1/(5x^2 + 9y^2)(18y)) = 10x/(5x^2 + 9y^2)
y' = 180xy / (18y(5x^2+9y^2) - 1)
y = ln(5x^2 + 9y^2).
y' = 1/(5x^2 + 9y^2) * (10x + 18yy')
y' (1 - 1/(5x^2 + 9y^2)(18y)) = 10x/(5x^2 + 9y^2)
y' = 180xy / (18y(5x^2+9y^2) - 1)