Suppose that x=x(t) and y=y(t) are both functions of t. If y^2+xy−3x=29, and dy/dt=−3 when x=−5 and y=−2, what

Suppose that x=x(t) and y=y(t) are both functions of t. If
y^2+xy−3x=29,
and dy/dt=−3 when x=−5 and y=−2, what is dx/dt?

Not sure how to this question. Thanks!

The given function is
y^2+xy−3x=29
differentiating it with respect to t
2y.dy/dt + y.dx/dt + x.dy/dt -3.dx/dt=0 ...(1)
SINCE, dy/dt=−3 when x=−5 and y=−2
we get (1) as,
2(-2)(-3) -2.dx/dt -5.(-3) -3.dx/dt =0
Or, 12 +dx/dt +15=0
Or, -5dx/dt = -27
Or dx/dt = 27/5
Hope its the right answer

use implicit differentiation, so y^2+xy−3x=29 becomes: 2ydy/dt + xdy/dt + ydx/dt - 3dx/dt =0. then just plug in -3 for dy/dt, -5 for x, and -2 for y and solve for dx/dt