Find y' if y = ln(7x^2+3y^2)

Question

Find y' if y = ln(7x²+3y²)

y'=_______

Answer 1

First, exponentiate both sides to get:

e^y = 7x² + 3y²

Separating the variables, we have:

e^y - 3y² = 7x²

Taking the derivative of both sides, we have:

(e^y - 6y)y' = 14x

Therefore, we have:

y' = 14x/(e^y - 6y)