You do the implcit differentation, then solve for y' and check where this is defined.
In your case: Differentiate implicitly: 2xy + x²y' - y² - x*2yy' = 0
Solve for y': y'(x²-2xy) +2xy - y² = 0
y' = (2xy-y²) / (x²-2xy)
Check where defined: y' is not defined if the denominator becomes zero, i.e.
x² - 2xy = 0 x(x - 2y) = 0
This has formal solutions x=0 and y=x/2. Now we check whether these values are possible for the initially given definition of y:
0^2*y - 0*y^2 =? 4 0 =? 4
This is impossible, hence the function is not defined for 0, and we can disregard this.
x^2*(x/2) - x(x/2)^2 =? 4 x^3/2 - x^3/4 = 4 x^3/4 = 4 x^3=16 x^3 = 16 x = cubicroot(16)
This is a possible value for y, so we have a point where y is defined, but not y'.
The solution to all of it is hence D - { cubicroot(16) }, where D is the domain of y (which nobody has asked for in this example :-).
(Actually, the check whether 0 is in D is superfluous: If you write as solution D - { 0, cubicroot(16) }, this is also correct - only it so happens that 0 is not in D, so the set difference cannot take it out of there ...).
If someone asks for that D, you have to solve the definition for y and find that domain - I don't know of any [general] way to find the domain without solving for the explicit function).
Answer:
-7/2
Step-by-step explanation:
The slope of a line can be defined as: 
, which can be more formally calculated as: 
, where it's essentially the same thing, except the rise/run is being calculated with two points (which you already need)
So let's just say: 
Plugging the values into the equation we get: 
You can also just look at the graph and see that from point 1 to point 2, it "rised" -7 units, and "ran" 2 units.
Notice how the "rise" is negative? That just means it went down.
2 years=24 months
6000$/24 months=250$ saved per month
When you are adding or subtracting fractions with different denominators, you need to find a common denominator.
The LCD will be 11 x 14 which is 154.
So...
9/11 - 2/14 becomes 126/154 - 22/154.
126/154 - 22/154 = 104/154 = 52/77
answer: 52/77
