d gradient of d curve y=xy+2px+3qy at d point(3,2)is-2/3 find d value of p&q?

Question

its calculus problem.i want d way how to get this

Answer 1

dy/dx=d(xy)/dx+d(2px)/dx+d(3qy)/dx
d(xy)/dx=xdy/dx+y
dy/dx=xdy/dx+2p+3qdy/dx
dy/dx(1-x-3q)=2p
dy/dx=2p/(1-x-3q)
substitute values:
-2/3=2p/(1-3-3q)
4+6q=6p ---->eq1

y=xy+2px+3qy
subs values:
2=6+6p+6q
6p+6q= -4 -->eq2
Solve:
subs eq1 into eq2
6q+4+6q= -4
12q= -8
q= -2/3
p=6q+4
p=-4+4
p=0
Ans: p=0 q= -2/3

Answer 2

dy/dx=xdy/dx+y+2p+3qdy/dx

dy/dx = dy/dx (x + 3q) +y + 2p (1)

or dy/dx [1 - (x + 3q)] = y +2p (2)

when x = 3, y= 2 and dy/dx = -2/3

plugging into (2) -2/3 (1 -3 +3q) = 2 + 2p

or 2 - 3q = 3 + 3p

or p + q = -1/3

Answer 3

I know the answer but I dont have the time to explain it. I have to study for my pre boards. So if you want you can mail me the question at [e-mail] and I'll mail you the scanned solution. You can have a look at it then.