Final answer:
To solve for dy/dt when x = 2 and y = -5, differentiate the given equation using implicit differentiation and substitute the given values to solve for dy/dt.
Step-by-step explanation:
To find dy/dt when x = 2 and y = -5, we need to differentiate the given equation with respect to t using implicit differentiation.
Start by taking the derivative of each term:
- d(y^2)/dt = 2y * (dy/dt)
- d(xy)/dt = x * (dy/dt) + y * (dx/dt)
- d(-3x)/dt = -3 * (dx/dt)
- d(9)/dt = 0
Now substitute the given values to solve for dy/dt:
2(-5) * (dy/dt) + 2 * (-2) + (-3) * 0 = 0
-10(dy/dt) - 4 = 0
-10(dy/dt) = 4
dy/dt = 4/-10 = -2/5