Related Rates Formula: Solving for dx/dt with xy^2 = 12 and dy/dt = 6

[Nitrate]

Homework Statement

If xy^2 = 12 and dy/dt = 6, find dx/dt when y = 2.

Homework Equations

The Attempt at a Solution

My teacher wants us to follow a five step method for solving related rates:
Step 1 [Information]:
Assign variable letters to known and unknown quantities
xy^2 = 12
dy/dt = 6
dx/dt = ?
y = 2

Step 2 [Formula]:
Find or develop a formula that relates the main variables in the problemStep 3 [Variable Check]: Eliminate variables, if possible*:
i) substitute constant values** or
ii) use another relation between the variables

Step 4 [Differentiation]: Differentiate the formula with respect to time, and solve for he unknown rate.

Step 5 (solving): substitute known (instantaneous) values, calculating them from given info, if necessary.

Step 6 (answer): state the answer to the problem

I'm not sure where to go from step 2.

 

[Dick]

Skip to step 4. Differentiate x*y^2=12 with respect to t. Then go from there.

 

[Nitrate]

Skip to step 4. Differentiate x*y^2=12 with respect to t. Then go from there.

dx/dt = (dy/dx)(dy/dt)
dx/dt = (-y/2x)(dy/dt)
dx/dt = (-(2)/2x)(6)
dx/dt = -6x?

 

[Dick]

dx/dt = (dy/dx)(dy/dt)
dx/dt = (-y/2x)(dy/dt)
dx/dt = (-(2)/2x)(6)
dx/dt = -6x?

Mmm. No. x(t)*y(t)^2=12. Take d/dt of both sides. On the right side d/dt 12=0. That's easy. On the left side you'll need to use the product rule and the chain rule.