Please help with implicit differentiation

i'm currently studying for an exam which is in 2 weeks
my question is how to do this
x^2+axy^2+by^3=1 with a point (3,2) and gradient of -1 at that point.

x^2 + axy^2 + by^3 = 1

x = 3
y = 2

3^2 + a * 3 * 2^2 + b * 2^3 = 1
9 + 12a + 8b = 1
12a + 8b = -8
3a + 2b = -2


x^2 + axy^2 + by^3 = 1
2x * dx + a * (x * 2y * dy + y^2 * dx) + b * 3y^2 * dy = 0

x = 3
y = 2
dy/dx = -1

2 * 3 * dx + a * (3 * 2 * 2 * dy + 2^2 * dx) + b * 3 * 2^2 * dy = 0
6dx + a * (12dy + 4dx) + 12b * dy = 0
6 * dx + 12a * dy + 4a * dx + 12b * dy = 0
dy * (12a + 12b) + dx * (6 + 4a) = 0
dy * (6a + 6b) + dx * (3 + 2a) = 0
dy * (6a + 6b) = -dx * (3 + 2a)
dy/dx = -(3 + 2a) / (6a + 6b)
-1 = -(3 + 2a) / (6a + 6b)
1 = (3 + 2a) / (6a + 6b)
6a + 6b = 3 + 2a
4a + 6b = 3


3a + 2b = -2
4a + 6b = 3

3 * (3a + 2b) = 3 * (-2)
9a + 6b = -6
6b = -6 - 9a

4a + 6b = 3
6b = 3 - 4a

-6 - 9a = 3 - 4a
-6 - 3 = 9a - 4a
-9 = 5a
a = -9/5

4a + 6b = 3
-36/5 + 6b = 15/5
6b = 51/5
b = 51/30
b = 17/10

sorry:
I can't helping
I am brasilian
end not inglish