find dydx of
x^2 + 3xy + 2y^2 = 5
My working
2y^2 = 5 - x^2 - 3xy
y^2 = 1/2 . (5 - x^2 - 3xy)
y = root 1/2 . (5 - x^2 - 3xy)
y = 1/2 . (5 - x^2 - 3xy)^1/2
y = (2.5 - 1/2x^2 - 1.5xy)^1/2
y1 = 1/2 (2.5 - 1/2x^2 - 1.5xy)^-1/2. 3
Advice please if i am close
Cheers
Just to clarify a bit on what skeeter is saying:
To use the more "traditional" method of solving for a derivative, you would need to solve for y explicitly. What that means is that you can get the equation into the form where there are no terms on the right hand side at all.
Although your work to solve for seemed like it was on the right track, the problem is you are stuck with a term in the right hand side.
The correct way to handle this problem is to use implicit differentiation. This method is used without first solving for .
Just to give you a small hint -- You do not need to simply or modify the equation at all before taking the derivative! Have you learned implicit differentiation techniques?
When you have , it is the same as evaluating except that there is a attached (multiplied).
So deriving gives
This is simply a special case of the chain rule: notice that when evaluating x's this rule is hidden by the fact .
Product rules with work as you would expect. Can you use this technique to answer your question?