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

Click For Summary
To solve for dx/dt given the equation xy^2=12, first express x as a function of y: x=12/y^2. Then, differentiate both sides with respect to t using the chain rule, resulting in the equation (y^2)(dx/dt) + x(2y)(dy/dt) = 0. Substitute y=2 and dy/dt=6 into the equation to find dx/dt. The correct calculations yield dx/dt when y=2, providing the desired rate of change.
dcgirl16
Messages
27
Reaction score
0
If xy^2=12 and dy/dt=6, find dx/dt when y=2

The way i thought to do this would be
(1)(y^2)+x(y)(dy/dt)=0 but i don't know x so this isn't working, what am i doing wrong
 
Physics news on Phys.org
You just multiply the derivative of x with respect to y by 6(chain rule). You can find x as a function of y by solving for it so x=12/y^2.
 

Similar threads

Graduate Non solvable integral? (dx/dt)^2 dt
  • · Replies 3 ·
Replies
3
Views
3K
Finding the rate of change of x in the equation
  • · Replies 8 ·
Replies
8
Views
1K
Undergrad Integral confusion for a simple Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
MHB How to Solve Related Rates Problems in Calculus 1
  • · Replies 8 ·
Replies
8
Views
4K
MHB 1.3 find dx of (7+9x-6\sqrt{x})/x
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Partial Derivative of Convolution
  • · Replies 2 ·
Replies
2
Views
3K
MHB Find rate of change (Why is my answer wrong?)
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Second derivative of a curve defined by parametric equations
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving for d^2y/dt^2: Finding d^2y/dt^2 with dx/dt=1/2
  • · Replies 1 ·
Replies
1
Views
4K
MHB How to Perform Implicit Differentiation on \(x^2-4xy+y^2=4\)?
  • · Replies 1 ·
Replies
1
Views
1K