Question

Erggh I keep getting it wrong? Implicit differentiation?

Answer 1

If x^2-2xy+3y^2=8 then dy/dx =?

Answer 2

I used the product rule

Answer 3

ok, implicit differentiation is another application of the chain rule

Answer 4

and you will use the product rule too for the 2xy term

Answer 5

let me type a bit of it out...

Answer 6

2x-2y+dy/dx*x+6y*dy/dx

Answer 7

\[2x-2y=\frac{ dy }{ dx }(-x-6y)\]

Answer 8

So I get \[\frac{ 2x-2y }{ -x-6y }\]

Answer 9

But it's not one of my answer choices ;'(

Answer 10

\[\frac{ d }{ dx }x^2 -[ 2x\frac{ d }{ dy }y*\frac{ dy }{ dx } + y*\frac{ d }{ dx }2x] + \frac{ d }{ dy }3y^2*\frac{ dy }{ dx } = \frac{ d }{ dx }8\]

Answer 11

you see how the chain rule works, for y terms w.r.t. x

\[\frac{ d }{ dy }*\frac{ dy }{ dx }\]

first take the derivative w.r.t. Y, then y with respect to x

Answer 12

so overall you get d/dx

Answer 13

The middle term 2xy is the one in brackets, product rule

Answer 14

\[2x - [ 2x*(1) \frac{ dy }{ dx } + y *2] + 6y \frac{ dy }{ dx } = 0\]

Answer 15

To verify your answer,
\[\frac{dy}{dx}=\frac{x-y}{x-3 y}\]

Answer 16

solve for dy/dx

Answer 17

\[2x - 2x \frac{ dy }{ dx } - 2y+ 6y \frac{ dy }{ dx } = 0\]

Answer 18

did i mess something up?

Answer 19

\[2x-2y+2x*\frac{ dy }{ dx }+6y*\frac{ dy }{ dx }\]

Answer 20

\[\frac{ dy }{ dx }(2x+6y)=-2x+2y\]

Answer 21

\[\frac{ dy }{ dx }=\frac{ -2x+2y }{ 2x+6y }\]

Answer 22

I didn't get x−y/x-3y :(

Answer 23

i think you messed up a sign somewhere.

Answer 24

ohhh I got it this time!!! :D

Answer 25

yeah, the second term is subtracted, put the entire product rule in parenthesis, that is the sign you missed

Answer 26

yayyy thanks so much guys ^_^

Answer 27

look at my last step, that is correct after you simplify and solve for dy/dx

Answer 28

cool, your welcome

Answer 29

remember parenthesis, and the negative distributes to each term in the product rule

Answer 30

^_^

Answer 31

\[2x - 2y + (6y - 2x)\frac{ dy }{ dx } = 0\]

Answer 32

\[\frac{ dy }{ dx } = \frac{ -2x + 2y }{ 6y - 2x }\]

Answer 33

pull out a negative and a 2 from everything , and cancel, it ends up good

Answer 34

\[\frac{ dy }{ dx } = \frac{ -2(x-y) }{ -2(x-3y) } = \frac{ x-y }{ x-3y }\]

Answer 35

That was the answer you were looking for right?

Answer 36

well there is an option: y-x/3y-x

Answer 37

right, just leave the negatives in for that answer

Answer 38

multiply above by (-1)/(-1)

Answer 39

THe original one i had was
\[\frac{ dy }{ dx } = \frac{ -2x + 2y }{ 6y - 2x }\]

just take a common factor 2 out, to get your final answer