anonymous
  • anonymous
Given xy=-9 find dy/dt when x = -7 and dx/dt=-7
Calculus1
schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
the answers are in the screen shot
anonymous
  • anonymous
are you still there?

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anonymous
  • anonymous
>>>???
Australopithecus
  • Australopithecus
dy/dt xy = -9 dy/dt xy = -9 xy' = -9 y' = 9/7
Australopithecus
  • Australopithecus
dx/dt xy = - 9 yx' = - 9 y(-7) = - 9 y =-9/-7 y = 9/7
Australopithecus
  • Australopithecus
I think this is right just using implicit differentiation
Australopithecus
  • Australopithecus
and chain rule
Australopithecus
  • Australopithecus
do you understand how I got my answer?
anonymous
  • 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
  • Australopithecus
ok send me a link to your next question
zepdrix
  • 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
  • anonymous
austra i sent you a mail
Australopithecus
  • 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
  • anonymous
no lol.
zepdrix
  • zepdrix
No both are variables, unless you're taking a partial derivative, you need to apply the product rule.
anonymous
  • anonymous
both are functions of time.
zepdrix
  • 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
  • Australopithecus
oh I guess so :)
anonymous
  • anonymous
d/dt( x*y=-9) = dx/dt*y + x*dy/dt =0 dy/dt = -dx/dt *y/x
Australopithecus
  • Australopithecus
can you break down the steps clearer algebraic!
anonymous
  • anonymous
it's just use of the product rule on x*y =-9 then solving algebraically for dy/dt
zepdrix
  • 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
  • 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
  • anonymous
you do take the derivative on both sides and you do 'get 0'

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