If x^2 + xy = 20 and dx/dt = - 4 when x = - 5 and y = 1, what is dy/dt

3.2

Step-by-step explanation:

x² + xy = 20

Take the derivative with respect to time:

2x dx/dt + x dy/dt + y dx/dt = 20

(2x + y) dx/dt + x dy/dt = 20

Given x = - 5, y = 1, and dx/dt = - 4:

(2 (-5) + 1) (-4) + (-5) dy/dt = 20

(-10 + 1) (-4) - 5 dy/dt = 20

36 - 5 dy/dt = 20

5 dy/dt = 16

dy/dt = 3.2