## hiramoby 3 years ago Given xy=-9 find dy/dt when x = -7 and dx/dt=-7

1. hiramoby

2. hiramoby

the answers are in the screen shot

3. hiramoby

are you still there?

4. hiramoby

>>>???

5. Australopithecus

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

6. Australopithecus

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

7. Australopithecus

I think this is right just using implicit differentiation

8. Australopithecus

and chain rule

9. Australopithecus

do you understand how I got my answer?

10. hiramoby

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

11. Australopithecus

12. 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

13. hiramoby

austra i sent you a mail

14. 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

15. Algebraic!

no lol.

16. zepdrix

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

17. Algebraic!

both are functions of time.

18. 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

19. Australopithecus

oh I guess so :)

20. Algebraic!

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

21. Australopithecus

can you break down the steps clearer algebraic!

22. Algebraic!

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

23. 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

24. 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

25. Algebraic!

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