Find y' for y = y(x) defined implicitly by

Question

Find y' for y = y(x) defined implicitly by 

Answer 1

Differentiating both sides of the equation and using the product rule for the first term gives

3( 1 * y + y' * x) - 2x = 0

3(y + xy') = 2x

y + xy' = (2/3)x

xy' = (2/3)x - y

y' = (2/3) -y/x

If we solve for y using the original equation and substitute above, we can get y' in terms of x.

y = x/3 + (4/3x)

y' = 1/3 - 4/(3x²)

Answer 2

desmos.com/calculator/ueqtitkmgb