help me get the derivative of x^2-2xy+3y^2...i have no idea?

Answer 1

This problem is incomplete. x^2 - 2xy + 3y^2 is just an expression, not a function or a curve. If this expression were set equal to something, you could find the derivative by simply taking the derivative of both sides and using algebra to get an expression in terms of x and y. As it is, you cannot find the derivative of the expression, because none exists.

You sent me a message with the other half of the equation. Knowing that the full problem is x^2 - 2xy + 3y^2 = 8, we can differentiate both sides. Remember that the derivative of y is dy/dx, and that we will have to apply the chain rule for functions of y. So 2x - 2y + 6y(dy/dx) = 0, noting that d/dx(3y^2) = d/dy(3y^2)*dy/dx, and that the derivative of a constant is 0. So we see that 6y(dy/dx) = 2y - 2x, and dy/dx = 1/3 - x/(3y).

Answer 2

For this problem, you need to use Implicite Differentiation (since you are dealing with x's and y's). As you may know, you can take the derivative of each individual part and treat it as an individual differentiation problem. First, we can take the derivative of the x^2 which will be 2x. However, when you have -2xy, you need to use the product rule since you are multiplying x times y by a factor of 2. While this is a product, don't forget that the derivative of y will be y' or (if you wish to write, dy/dx). Secondly, the derivative of 3y^2 will be (6y)(dy/dx) or (6y)(y').

Hope this helps let me know if you have any further questions!

Andrew

Answer 3

If you mean the factors, they would be (x-3y) and (x+y). Ah...sweet Algebra 2!

Answer 4

Use implicit differentiation:
shouldn't there be another side to the equation so you can solve for y' ?

Answer 5

differentiate term by term
2x-(2xy'+y)+6yy'

Answer 6

Wow, does that look hard!! I wish I could help, but I'm no Albert Einstein (in math).