## moongazer 2 years ago If y^3 = at^2 , then (d^2 y)/dt^2 ?

1. moongazer

I only got to the part: dy/dt = 2at/3y^2

2. Yttrium

Just derive again, so you can solve the d^2y/dt^2. :))

3. Yttrium

it's like solve for y''

4. amriju

let it remain as 3y^2=2at..differntiate again....using multiplication rule....

5. moongazer

it says the answer is: -2a/9y^2 but I am getting a different answer

6. moongazer

is "a" here constant?

7. Yttrium

Quotient rule, remember?

8. amriju

yo constnt

9. Yttrium

for easier calculation, you can factor out 2a/3 and just derive (t/y^2)

10. moongazer

could you show me the first step for the second derivative? maybe I did something wrong

11. moongazer

i'll try again :)

12. amriju

may be u need to substitute y as (at^2)^2/3

13. moongazer

I got: (6ay^4 - 8a^2 t^2 y)/9y^6 I think I am doing something wrong.

14. moongazer

i'll try again :)

15. Yttrium

$y' = \frac{ 2at }{ 3y^2 }$, right? Therefore, $y' = \frac{ 2a }{ 3 } (\frac{ t }{ y^2 })$ $y'' = \frac{ 2a }{ 3 } [\frac{ y^2 - 2tyy') }{ y^4 }]$ $y'' = \frac{ 2a }{ 3 } \frac{ y^2 - 2ty(\frac{ 2a }{ 3 })(\frac{ t }{ y^2 }) }{ y^4 }$ Simplifying this equation we will get. $y'' = \frac{ 2a }{ 3 } [ \frac{ 3y^4 -4at^2y }{ 3y^6 }]$

16. Yttrium

17. moongazer

That's what I got. I think there is some typo in my answer sheet. Thanks :)

18. myininaya

Well you could simplify

19. Yttrium

@moongazer, it isn't the answer in simplest form. Maybe you can continue this and let us verify if we get the same answers.

20. moongazer

@myininaya could you simply it further? @Yttrium yes, I understood your solution

21. myininaya

Could I? Yes. Can you?

22. myininaya

Eye ball the numerator and the denominator. You should see they share a common factor.

23. Yttrium

For our class, the definition of simplest form is that it is factored out completely. Just factor out some stuff and do cancellation.

24. moongazer

2a(3y^3 - 4at^2) / 9y^5

25. moongazer

that's what I got

26. myininaya

You can also choose to write at^2 as y^3

27. myininaya

Recall our initial equation: y^3=at^2

28. myininaya

I see at^2

29. myininaya

Replace it y^3 then combine like terms

30. Yttrium

@moongazer , do you what myininaya told you?

31. myininaya

@moongazer I'm leaving for tonight but I think Yttrium is still here to help. Goodnight you guys. I think you guys got it from here for sure. :)

32. moongazer

WOW! Thank you very much to both of you. I failed to notice that until you said it. Thanks :) I now got the answer. :)