find dy/dx :

Question

x^3 + 4x^2 y^2 = 3x^2 -2(x + y)

 

Maybe using Implicit differentiation? 

Answer 1

You are correct.  We can use implicit differentiation here.  Derive both sides of the equation using the chain rule.  Be sure to distribute the terms on the right side of equation first.

 

(x³ + 4x²y²)' = (3x² - 2x - 2y)'

 

3x² + 8xy² + 8x²yy' = 6x - 2 - 2y'

 

 

Now just move all the y' terms to one side of equation and all the non-y' terms to the other side of equation.

 

Factor out a y'.  This is the GCF of the y' terms.

 

Then divide both sides of the equation by the coefficient of y'.