Simplifying the second derivative I need to simplify the below with respect to y′′. I'm given:y''=-(3x^2y^3-3x^3y^2(-(x^3)/(y^3)))/(y^6} The final result should look like: -(3x^2(y^4+x^4))/(y^7)

anudoneddbv 2022-07-18 Answered
Simplifying the second derivative
I need to simplify the below with respect to y . I'm given:
y = 3 x 2 y 3 3 x 3 y 2 ( x 3 y 3 ) y 6
The final result should look like:
3 x 2 ( y 4 + x 4 ) y 7
Here are my steps:
1.Combine term: 3 x 3 y 2 ( x 3 y 3 )
3 x 3 y 2 ( x 3 y 3 ) = 3 x 6 y 2 y 3
Our expression is now:
y = 3 x 2 y 3 + 3 x 6 y 2 y 3 y 6
2.Multiply the final term in the numerator, 3 x 6 y 2 y 3 , by the it's reciprocal in the denominator, y 6 1 , to eliminate the complex fraction.
3 x 6 y 2 y 3 y 6 1 = 3 x 6 y 8 y 3
Our expression is now:
y = 3 x 2 y 3 y 6 + 3 x 6 y 8 y 3
3.Multiply term 3 x 6 y 8 y 3 by y 3 y 3 to make common denominators.
3 x 6 y 8 y 3 y 3 y 3 = 3 x 6 y 11 y 6
Our separate terms can now be added, and our expression will look like:
y = 3 x 2 y 3 + 3 x 6 y 11 y 6
4.Now factor the numerator, our expression will become:
y = 3 x 2 y 3 ( 1 + x 4 y 8 ) y 6
Have I made a mistake? I'm not sure where to go from here. I need to achieve this expression as stated at the top my question:
y = 3 x 2 ( y 4 + x 4 ) y 7
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Answers (1)

Kitamiliseakekw
Answered 2022-07-19 Author has 23 answers
y = 3 x 2 y 3 3 x 3 y 2 ( x 3 y 3 ) y 6 = 3 x 2 y 3 + 3 x 3 ( x 3 y ) y 6 = y = ( 3 x 2 y 4 + 3 x 6 y ) y 6 = 3 x 2 y 4 + 3 x 6 y 7 = 3 x 2 ( y 4 + x 4 ) y 7

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