Question

Assume that x and y are functions of t and x^2+2xy=5. If dx/dt=-3 when x=-1, find dy/dt

Answer 1

x^2+2xy=5
differentiate with respect to t
2x dx/dt + 2x dy/dt + 2y dx/dt = 0
x dx/dt + x dy/dt + y dx/dt = 0

when x = -1 in the original:
1 + 2(-1)y = 5
-2y = 4
y = -2

so we have dx/dt = -3, x = -1, y = -2
then in
x dx/dt + x dy/dt + y dx/dt = 0
-1(-3) + (-1)dy/dt + (-2)(-3) = 0
3 - dy/dt + 6 = 0
dy/dt = 9

check my arithmetic