Calculate dy/dt using the given information. xy + x = 12; dx/dt = -3, x = 2, y = 5?
To calculate dy/dt using the given information, we need to use implicit differentiation.
Given the equation xy + x = 12, we can differentiate both sides with respect to t (time), using the chain rule for differentiation.
Differentiating the left side:
d/dt(xy) + d/dt(x) = d/dt(12)
Using the product rule, we get:
y * dx/dt + x * dy/dt + dx/dt = 0
Substituting the given values:
5 * (-3) + 2 * dy/dt + (-3) = 0
Simplifying the equation:
-15 + 2 * dy/dt - 3 = 0
2 * dy/dt - 18 = 0
Now, solve for dy/dt:
2 * dy/dt = 18
dy/dt = 18/2
dy/dt = 9
Therefore, dy/dt is equal to 9.
x y + x = 12
x dy/dt + y dx/dt + dx/dt = 0
2 dy/dt + 5(-3) - 3 = 0
I guess you can take it from there.