Question

suppose xy=3 and dy/dt=4. find dx/dt when x=-2

Answer 1

I got 16/3

Answer 2

(dy/dt)/(dx/dt)=dy/dx
Solve for y when x =-2 for starters
then find dy/dx implicitly.

Answer 3

I don't know how to do that? :/

Answer 4

Can you tell me how like generally so i can solve it?/

Answer 5

Starting by solving for y?

Answer 6

doesn't y=3?

Answer 7

xy=y?

Answer 8

when x=2?\[xy=3\]\[-2y=3\]

Answer 9

-3/2

Answer 10

yes. Now you have an ordered pair (-2, -3/2) which will come in handy later.

Answer 11

Can you differentiate implicitly?

Answer 12

No, that's what I don't understand at all.

Answer 13

Well, you could say that all differentiation is implicit, because when we differentiate implicitly we treat the y as a variable to be differentiated, with all the usual rules in effect. \[\frac{ d }{ dx }(y)=\frac{ dy }{ dx }\] What we'll do, though instead of using the product rule on xy, is solve for y and differentiate. That should be easier. So,\[xy=3\]\[y=\frac{ 3 }{ x }\]Can you differentiate that?

Answer 14

You could also write the x with a negative exponent if you prefer the power rule

Answer 15

-3/x^2?

Answer 16

Yeah. When you substitute x=-2, you get the slope, or dy/dx, which I said earlier was equal to (dy/dt)/(dx/dt)

Answer 17

3/4

Answer 18

negative

Answer 19

4=3/4*dx/dt?

Answer 20

oh -3/4

Answer 21

otherwise you're right. Just solve.

Answer 22

19/4

Answer 23

You dropped the negative sign, and where did you get 19??

Answer 24

4+3/4?

Answer 25

my calculator gave me 19/4

Answer 26

You weren't supposed to add. 4=dy/dt. -3/4=dy/dx. dy/dx=(dy/dt)/(dx/dt). dx/dt=?

Answer 27

-16/3, I got it...