Question

find dx/dt of xy=4. when x=1 and dy/dt=-6

Answer 1

@KeelyLynn ready?

Answer 2

yes

Answer 3

Show me how far you've got with this problem.

Answer 4

\[dx \div dt= 4 div y\]
\[=4y ^{-1}=-4y ^{-2}dx \div dt\]

Answer 5

then i insert the given numbers for y & dy/dt and i dont get the right answer

Answer 6

sorry that last dx/dt is suppose to be dy/dt

Answer 7

No. Remember that you are differentiating all variables with respect to time.

Answer 8

OK, so what you did is first rewrite xy = 4 as\[y =\frac{ 4 }{ x }\]Correct? This is fine. Remember that the product rule is another option.

Answer 9

I'm sorry, I meant, you rewrote the function as

Answer 10

\[x =\frac{ 4 }{ y }\]

Answer 11

yes

Answer 12

OK that's fine. Then after differentiation, you obtained\[\frac{ dx }{ dt }=\frac{ -4 }{ y ^{2} }\frac{ dy }{ dt }\]This is correct.

Answer 13

What do you think you should do next?

Answer 14

i moved the y^2 to the top making y^-2

Answer 15

i mean moved the y to the top making y^-1

Answer 16

oh i see what you did. moved the y^-2 after differeiation to the bottom to make it positive

Answer 17

i just realized it gives me find dx/dt when x=1..but theres no x?

Answer 18

Yes. Look! You're given x = 1 and dy/dt = -6. What you need to find is dx/dt but you don't know y. How will you find the value of y? That is an important question here.

Answer 19

im not sure

Answer 20

@KeelyLynn please think about it. You need the value for y to solve for dx/dt. How will you do that. Hint: Use the given equation.

Answer 21

Substitute x = 1 into the original equation, and solve for y.

Answer 22

isolate y? and plug in the given value for x. to find y

Answer 23

so y=4

Answer 24

Yes!

Answer 25

Now find dx/dt. What is the solution?

Answer 26

3/2

Answer 27

Perfect. I knew you could do it! Excellent work!!

Answer 28

@KeelyLynn do you have a better understanding of these problems, now?

Answer 29

yes thank you!