Question

Determine dy/dt for xy + x = 12, given x= 2 , y =5 , and dx/dt = -3

Answer 1

?

Answer 2

yes calculus

Answer 3

Tough one ... For me anyway Lol

Answer 4

Is it written, right though?

Answer 5

says solve the problem

Answer 6

Determine dy/dt for xy + x = 12 given x = 2, y = 5, and dx/dt = -3.

Answer 7

have you tried it?

Answer 8

I don't know where to start. I believe you use chain rule but unsure

Answer 9

maybe implicit differentiation to find dy/dx first?

Answer 10

yes

Answer 11

Im just guessing tho lol..havent done these in a while so
\[\frac{dy}{dx}=\frac{-y-1}{x}\]
according to: http://www.wolframalpha.com/input/?i=+differetiate++xy+%2B+x+%3D+12+

Answer 12

then sub in \(x=2,y=5\)
then you have your dy/dx

then use the chain rule to find dy/dt

Answer 13

This doesn't actually look like a diff eq, @Mimi_x3. It looks like an exercise for implicit differentiation.

Answer 14

\[\text{Given }xy+x=12,\text{ find }\frac{dy}{dt}\text{ when }x=2,y=5,\text{ and }\frac{dy}{dt}=-3.\\
\frac{d}{dt}\left[xy+x \right]=\frac{d}{dt}[12]\\
\frac{d}{dt}[xy]+\frac{d}{dt}[x]=\frac{d}{dt}[12]\\
\left(\frac{d}{dt}[x]y+x\frac{d}{dt}[y]\right)+\frac{d}{dt}[x]=\frac{d}{dt}[12]\\
(y+1)\frac{dx}{dt}+x\frac{dy}{dt}=0\]
Now substitute the given values and solve for the remaining variable.

Answer 15

I know; I realised. But, I think it should be done like this. :)\[\frac{dy}{dt}=\frac{dy}{dx}*\frac{dx}{dt}\]
\[\frac{dy}{dx}=\frac{-y-1}{x} => \frac{-5-1}{2} = -3\]
\[\frac{dy}{dx}=-3*-3 =9\]