Question

If 2x³ - xy + 3y² = 21 and (dy/dt) = -3 when x = 2 and y = -1, what is (dx/dt)?

Answer 1

To find (dx/dt), differentiate the given equation implicitly with respect to t and plug in the given values. The value of dx/dt is -4/3.

Step-by-step explanation:

To find (dx/dt), we first need to differentiate the given equation 2x³ - xy + 3y² = 21 implicitly with respect to t. Differentiating both sides of the equation gives:

6x²(dx/dt) - x(dy/dt) + 6y(dy/dt) = 0

Now, we are given that (dy/dt) = -3 when x = 2 and y = -1. Plugging in these values:

6(2)²(dx/dt) - 2(-3) + 6(-1)(-3) = 0

Simplifying the equation further:

dx/dt = -rac{4}{3}