Question

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

Answer 1

the answers are in the screen shot

Answer 2

are you still there?

Answer 3

>>>???

Answer 4

dy/dt xy = -9

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

Answer 5

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

Answer 6

I think this is right just using implicit differentiation

Answer 7

and chain rule

Answer 8

do you understand how I got my answer?

Answer 9

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

Answer 10

ok send me a link to your next question

Answer 11

@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

Answer 12

austra i sent you a mail

Answer 13

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

Answer 14

no lol.

Answer 15

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

Answer 16

both are functions of time.

Answer 17

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

Answer 18

oh I guess so :)

Answer 19

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

Answer 20

can you break down the steps clearer algebraic!

Answer 21

it's just use of the product rule on x*y =-9

then solving algebraically for dy/dt

Answer 22

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