Question

Evaluate dy/dt for 2xy-2x+2y^3=-10 with the conditions dx/dt=-4 x=2 y=-1

dy/dt=?

Answer 1

use implicit derivatives ....
2x dy/dt + 2y dx/dt + 6y^2 dy/dt = 0
now just plug in the given stuff.

Answer 2

I keep getting -4/5 which is incorrect.
2(2)dy/dt+(2)(-1)(-4)+6(-1)^2=0
10 dy/dt+8=0
10dy/dt=-8

Answer 3

dos soluciones para cada ecuacion
x-y=7

y=x-4

y=2-3x

Answer 4

Just curious. How do you get from

2(2)dy/dt+(2)(-1)(-4)+6(-1)^2=0

to

10 dy/dt+8=0

???

Answer 5

your 2(2)dy/dt+(2)(-1)(-4)+6(-1)^2=0
should have been
2(2)dy/dt + 2(-1)(-4) + 6(-1)^2 dy/dt = 0
4 dy/dt + 8 + 6dy/dt = 0
10dy/dt = -8
dy/dt = -4/5

I don't see any errors.

Answer 6

just notice I skipped the -2x term
so our derivative should be .

2(2)dy/dt + 2(-1)(-4) - 2dx/dt + 6(-1)^2 dy/dt = 0
2(2)dy/dt + 2(-1)(-4) - 2(-4) + 6(-1)^2 dy/dt = 0
4dy/dt + 8 + 8 + 6dy/dt = 0
dy/dt = -16/10
= -1.6