Question

HW: d^2(y)/dx^2 for x^2 - y^2 = 5

Answer 1

Start by finding the first derivative, what do you get?

Answer 2

one sec...

Answer 3

2x?

Answer 4

No >_>

Answer 5

I came up with that because the derivative of -y^2 is 0

Answer 6

he, im lost :P

Answer 7

2x-2y(y')=0

y'=-2x/-2y=x/y

Answer 8

it cant be x/y because its for x^2 - y^2 = 5.

Answer 9

That was just the first derivative.

Answer 10

Now for the second we know that:
\[\LARGE \frac{dy}{dx}=\frac{x}{y}\]

Answer 11

So now find:
\[\LARGE \frac{d^2y}{dx^2}\]

Answer 12

im confused

Answer 13

On finding the derivative?

Answer 14

the second part d^2y/dx^2

Answer 15

You have to use the quotient rule

Answer 16

gosh my brain is spinning

Answer 17

i have to finish this paper to study on

Answer 18

Okay, I'll go step-by-step and see if that helps you?

Answer 19

ok

Answer 20

Okay, so we have:
\[\LARGE x^2-y^2=5\]
Now, we differentiate with respect to x:
\[\LARGE x^2(\frac{dy}{dx})-y^2(\frac{dy}{dx})=5(\frac{dy}{dx})\]
And get:
\[\LARGE 2x-2y(\frac{dy}{dx})=0\]
Now get the y' by itself:
\[\LARGE -2y(\frac{dy}{dx})=-2x\]
Divide by -2y and simplify:
\[\LARGE \frac{dy}{dx}=\frac{-2x}{-2y}=\frac{x}{y}\]

Make sense so far?

Answer 21

kinda so what after that?

Answer 22

Now we have to find the derivative of x/y, so we have to use the quotient rule:
\[\LARGE \frac{d^2y}{dx^2}=\frac{(y*x(\frac{dy}{dx}))-(y(\frac{dy}{dx})*x)}{y^2}\]
Simplify:
\[\LARGE \frac{d^2y}{dx^2}=\frac{(y*1)-(\frac{dy}{dx}*x)}{y^2}\]
Now we know from earlier that:
\[\LARGE \frac{dy}{dx}=\frac{x}{y}\]
So plug that in:
\[\LARGE \frac{d^2y}{dx^2}=\frac{y-(\frac{x}{y}*x)}{y^2}\]
Can you finish it?

Answer 23

no it looks really herd :| its gonna be like 5 somethin' mate. i can get that

Answer 24

is it -5/y?

Answer 25

Did you at least try? >_>

Answer 26

@Isaiah.Feynman Can you check my work? I think I might of messed up..

Answer 27

im not sure if iget it

Answer 28

no

Answer 29

im not sure how to get the final answ

Answer 30

I explained most everything .-.

Answer 31

ya, but im still not sure about the final answ

Answer 32

Well if you did all the work you should of gotten something like \[\LARGE y^3-x^2y\]

Answer 33

i dont think

Answer 34

Actually, I'm not 100% sure..

Answer 35

how do you make it all pretty like that luigi0210

(y^2)-(x^2) divided by y^3 is what I got for the second derivative

Answer 36

its gotta be like 5 somethin'

Answer 37

@cc3 \[\LARGE LaTex\]
my friend~

Answer 38

its like 5 divided by somethin'

Answer 39

love ya mate i think i got its gonna be mighty helpful for tomorrows quiz

Answer 40

-.-