Given xy=-9 find dy/dt when x = -7 and dx/dt=-7

- anonymous

Given xy=-9 find dy/dt when x = -7 and dx/dt=-7

- schrodinger

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- anonymous

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- anonymous

the answers are in the screen shot

- anonymous

are you still there?

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## More answers

- anonymous

>>>???

- Australopithecus

dy/dt xy = -9
dy/dt xy = -9
xy' = -9
y' = 9/7

- Australopithecus

dx/dt xy = - 9
yx' = - 9
y(-7) = - 9
y =-9/-7
y = 9/7

- Australopithecus

I think this is right just using implicit differentiation

- Australopithecus

and chain rule

- Australopithecus

do you understand how I got my answer?

- anonymous

Thank you, help me with my other question please.
Yes I did , i was stuck after implicit.. thought it could not be this easy

- Australopithecus

ok send me a link to your next question

- zepdrix

@Australopithecus I'm confused by what you did in your steps. When you took the derivative, did you remember to apply the product rule? :o

- anonymous

austra i sent you a mail

- Australopithecus

I dont need to apply the product rule because we are taking the derivative in respect to t not in respect to y or x so they are treated as constants

- anonymous

no lol.

- zepdrix

No both are variables, unless you're taking a partial derivative, you need to apply the product rule.

- anonymous

both are functions of time.

- zepdrix

I did the steps using the product rule and I also came up with 9/7... so maybe just a little bit of luck XD lol

- Australopithecus

oh I guess so :)

- anonymous

d/dt( x*y=-9) = dx/dt*y + x*dy/dt =0
dy/dt = -dx/dt *y/x

- Australopithecus

can you break down the steps clearer algebraic!

- anonymous

it's just use of the product rule on x*y =-9
then solving algebraically for dy/dt

- zepdrix

|dw:1351050464937:dw|
Leibniz notation (with the differentials) can be a little tricky to understand. Maybe if you see it with the primes it'll make some sense :o

- Australopithecus

yeah that makes a lot more sense seeing as I had to take the derivative on both sides of the equation and I kept getting 0
Thanks for the refresher

- anonymous

you do take the derivative on both sides and you do 'get 0'

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