Question

evaluate dy/dt for the function at the point.
xy^2=4; dx/dt=-5, x=4, y=1
Answers: 5/8, 8/5, -5/8, -8/5

Answer 1

So what part are you stuck on?
Have you tried taking a derivative yet?

Need to apply product rule on the left.

Answer 2

i've got the derivative of the function, but i don't know what to do to get the dt part.

Answer 3

We're taking our derivative with respect to t, which means `both` x and y when we take their respective derivatives should give us prime terms, or dx/dt and dy/dt.

So taking the derivative gives us:

(x)'y^2 + x(y^2)' = (4)'

(1)x'y^2 + x(2y)y' = 0

Or if you want it written in Leibniz Notation:

(dx/dt)y^2 + 2xy(dy/dt) = 0

Does that look like what you came up with?

Answer 4

yeah. so now what do I do?

Answer 5

We have 4 unknowns in that derivative.
They provided us with information for 3 of the pieces and we need to solve for the 4th.

x = 4
y = 1
dx/dt = -5

Just plug them in and solve for the other one.

Answer 6

oh, I see! Thank you so much! I've been waiting for an hour, and now I can finally get to bed!

Answer 7

XD

Answer 8

I'm serious! I was waiting on one problem for an hour. You saved me another hour or two of waiting. So thank you again.

Answer 9

np c: go to bed!