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:
can you plz picture the graph so my answer you correctly .
Answer:
Make it as simple as possible, and use 1 and −1 .
1×1×1×1×1×−1×−1×−1×−1×−1=
15×(−1)2×(−1)2×−1=
1×1×1×−1=
−1.
So, the sign will be negative.
Another way of thinking about this is to not even think about the positive integers, as they won’t affect the sign. A positive integer times a positive integer is still a positive integer; a negative integer times a positive integer is still a negative integer.
So, you have five negative integers. Think of it like two negative integers, two more negative integers, and a single negative integer. Since two negative integers form a positive integer, you now have a positive, positive, and negative integer. This forms a negative sign.
Answer:
X=17
Step-by-step explanation:
7x-1+5x-23=180
12x-24=180
12x=204
x=17
0.571428571428...
571428 is repeating
