If xy=4 and dy/dy=3 then find dx/dt when x=4?
Your statement dy/dy = 3 must be wrong.
Did you mean dy/dt = 1?
I will assume you did.
dx/dt = dx/dy * dy/dt
= (dy/dt) / (dy/dx)
dy/dx = -4/x^2 = -1/4 when x=4
Therefore dx/dt = 3/(-1/4) = -12 at x=4
Oh my bad. I meant dy/dt.
I understand now. Thanks!
To find dx/dt when x=4, we need to differentiate both sides of the equation xy=4 with respect to t, using the chain rule.
We are given that dy/dt=3, which means that dy/dt represents the rate of change of y with respect to t.
Using the product rule, we can differentiate both sides of the equation xy=4:
d(xy)/dt = d(4)/dt
Applying the product rule, we get:
x(dy/dt) + y(dx/dt) = 0
Since we want to find dx/dt when x=4, we can substitute the given values into the equation. Let's do that:
4(dy/dt) + y(dx/dt) = 0
Since we are given dy/dt=3, we can plug it into the equation:
4(3) + y(dx/dt) = 0
Now we can solve for dx/dt:
12 + y(dx/dt) = 0
Substituting the value of y from the given equation xy=4, we have:
12 + 4(dx/dt) = 0
Simplifying the equation, we get:
4(dx/dt) = -12
Dividing both sides by 4, we find:
dx/dt = -3
Thus, when x=4, dx/dt is equal to -3.