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