Expert: Paul Klarreich - 3/21/2010

Question
Implicit differentiation

1)If 4y-2x=3x^2+y^2, then dy/dx=

and also...

2) What is the slope of the line tangent to the curves
3y^2 – 2x^2 = 6 – 2xy at the point (3, 2)?

Answer
Questioner: steve
Country: United States
Category: Calculus
Private: No
Subject: Implicit differentiation
Question: Implicit differentiation

1)If 4y-2x=3x^2+y^2, then dy/dx=

and also...

2) What is the slope of the line tangent to the curves
3y^2 – 2x^2 = 6 – 2xy at the point (3, 2)?
............................................

If  4y - 2x = 3x^2 + y^2, you differentiate each term.  Each time you see a 'y', there will be a dy/dx coming up.


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

4 dy/dx - 2 = 6x + 2y dy/dx

Now solve for dy/dx algebraically.  The answer will (normally) involve both x and y.

4 dy/dx - 2y dy/dx = 6x + 2

(4 - 2y) dy/dx = 6x + 2
        6x + 2
dy/dx = --------
        4 - 2y,
which you will simplify.

...........................................

2) What is the slope of the line tangent to the curves
3y^2 – 2x^2 = 6 – 2xy at the point (3, 2)?

Now you will:
1. find dy/dx.
2. evaluate it at (x=3,y=2) and get m.
3. Use m, x0=3, y0=2, to write the equation using:

y - y0 = m(x - x0)

You can finish up.