Hello,
Thank you for taking the time to read my post. I am following along with some example problems in my textbook, and I am very confused why I am getting a different answer than the textbook.
Problem is to find y'.
[MATH] x^3 + y^3 = 6xy[/MATH].
Solution:
Going to skip a bit on the solution to where I have the issue. Brief explanation - use sum rule and chain rule on left side to get:
[MATH] 3x^2 + 3y^2 y' [/MATH].
Right side use product rule to get:
[MATH] 6(xy' + y) [/MATH]Doing a bit of simplification we end up with:
[MATH] x^2 + y^2y' = 2xy' + 2y [/MATH]
The reason I am skipping the solution to this part is because this is essentially where I start to deviate from the textbook. I decided to solve for y' myself, without looking at what the textbook did, and I am very confused as to why I am not getting the same answer.
So, below is my attempt to solve for y'. I believe I am getting the wrong answer (please confirm) and I cannot figure out why.
Solving for y':
[MATH] x^2 + (y^2 y') = 2xy' + 2y [/MATH]
Step 1 - Move like terms onto the same side of the equal sign:
[MATH]x^2 - 2y = (2xy') - (y^2 y') [/MATH]
Step 2 - Factor out y' on the right hand side:
[MATH] x^2 - 2y = y'(2x - y^2) [/MATH]
Step 3 - Divide both sides by 2x-y^2:
[MATH] (x^2 - 2y)/(2x - y^2) = y' [/MATH]
When I looked up from this to check my work I saw that the textbook had done the following:
Solving from [MATH] x^2 + (y^2 y') = (2x y' + 2y) [/MATH]
1. Move like terms onto same side of the equal sign. Note that opposite terms were moved from how I did it.
[MATH] y^2 y' - 2xy' = 2y - x^2 [/MATH]
2. Factor y' out of the left hand side:
[MATH] y'(y^2 - 2x) = 2y - x^2 [/MATH]
3. Divide both sides by y^2 - 2x:
[MATH] y' = (2y - x^2) / (y^2 - 2x) [/MATH]
I don't understand what I did wrong and I'm feeling a bit like an idiot for not seeing it. I'm hoping you can help me discover my error.
Thank you for taking the time to read my post. I am following along with some example problems in my textbook, and I am very confused why I am getting a different answer than the textbook.
Problem is to find y'.
[MATH] x^3 + y^3 = 6xy[/MATH].
Solution:
Going to skip a bit on the solution to where I have the issue. Brief explanation - use sum rule and chain rule on left side to get:
[MATH] 3x^2 + 3y^2 y' [/MATH].
Right side use product rule to get:
[MATH] 6(xy' + y) [/MATH]Doing a bit of simplification we end up with:
[MATH] x^2 + y^2y' = 2xy' + 2y [/MATH]
The reason I am skipping the solution to this part is because this is essentially where I start to deviate from the textbook. I decided to solve for y' myself, without looking at what the textbook did, and I am very confused as to why I am not getting the same answer.
So, below is my attempt to solve for y'. I believe I am getting the wrong answer (please confirm) and I cannot figure out why.
Solving for y':
[MATH] x^2 + (y^2 y') = 2xy' + 2y [/MATH]
Step 1 - Move like terms onto the same side of the equal sign:
[MATH]x^2 - 2y = (2xy') - (y^2 y') [/MATH]
Step 2 - Factor out y' on the right hand side:
[MATH] x^2 - 2y = y'(2x - y^2) [/MATH]
Step 3 - Divide both sides by 2x-y^2:
[MATH] (x^2 - 2y)/(2x - y^2) = y' [/MATH]
When I looked up from this to check my work I saw that the textbook had done the following:
Solving from [MATH] x^2 + (y^2 y') = (2x y' + 2y) [/MATH]
1. Move like terms onto same side of the equal sign. Note that opposite terms were moved from how I did it.
[MATH] y^2 y' - 2xy' = 2y - x^2 [/MATH]
2. Factor y' out of the left hand side:
[MATH] y'(y^2 - 2x) = 2y - x^2 [/MATH]
3. Divide both sides by y^2 - 2x:
[MATH] y' = (2y - x^2) / (y^2 - 2x) [/MATH]
I don't understand what I did wrong and I'm feeling a bit like an idiot for not seeing it. I'm hoping you can help me discover my error.