Implicit Diff. answer check: x^2 - xy + y^2

[Lokito]

Hi. I'm having trouble with seeing what I'm doing wrong with a pretty simple implicit differentiation problem:

x^2 - xy + y^2 = 20

2x*dx/dx - (y*dx/dx + x*dy/dx) + 2y*dy/dx = 0

2x - y - x*dy/dx + 2y*dy/dx = 0
- x*dy/dx + 2y*dy/dx = -2x + y
dy/dx(-x + 2y) = -2x + y
dy/dx = (-2x+y)/(-x-2y)

Answer I've been given: -x/y

I don't think I did any of the individual components wrong, so I don't see how my answer isn't coming out right.

 

[soroban]

Hello, Lokito!

You made slight slip at the very end.
The denominator should have: \(\displaystyle 2y - x\)

Other than that, your approach is absolutely correct.

Did you look at the wrong answer?
Their answer is for a different equation: .\(\displaystyle x^2 + y^2 \:=\:C\)

 

[Lokito]

Hello, Lokito!

You made slight slip at the very end.
The denominator should have: \(\displaystyle 2y - x\)

Other than that, your approach is absolutely correct.

Did you look at the wrong answer?
Their answer is for a different equation: .\(\displaystyle x^2 + y^2 \:=\:C\)

I know, and that's why I thought it might be right. (It's close to my equation.)
I'm losing faith in Texas Instruments.

 

[Lokito]

Thanks.

I have another question on the second part of the same problem:

Find the coordinates of the points on the curve where the tangents are vertical.

I can do this if I have x alone. What do I do when I have both x and y to deal with in the derivative?

 

[Lokito]

edit: can I solve for y in terms of x using just the denominator of the derivative?

 

[Deleted member 4993]

edit: can I solve for y in terms of x using just the denominator of the derivative?

If interpret your "verbiage" correctly - you are correct.

It would have helped if you had shown mathematically - what you meant!!!

 

[Lokito]

edit: can I solve for y in terms of x using just the denominator of the derivative?

If interpret your "verbiage" correctly - you are correct.

It would have helped if you had shown mathematically - what you meant!!!

I tried it and didn't find the right answer.

2y -x = 0
2y = x
y = x/2

x/2 - x = 0
x = 0
I think I should have multiple points with vertical tangents.

 

[Deleted member 4993]

Hi. I'm having trouble with seeing what I'm doing wrong with a pretty simple implicit differentiation problem:

x^2 - xy + y^2 = 20

4y^2 - 2y^2 + y^2 = 20

y = +- sqrt(20)

x = +- 2*sqrt(20)

.