Find y' if y=ln(9x^2+7y^2).

Answer 1

well, just do it normally:

y' = 1/(9x^2+7y^2) * (18x+14yy')
Now just factor out the y' stuff.

Or, rewrite as

e^y = 9x^2 + 7y^2
e^y y' = 18x + 14yy'
y' = 18x/(e^y-14y)
= 18x/(9x^2+7y^2-14y)