Question

I need help with Applied Calculus 1, Find dy/dx by implicit differentiation.
(x^2)-6xy+(y^2)=6

Answer 1

\[x^2-6xy+y^2=6\]

Answer 2

hey

Answer 3

hello

Answer 4

so can i see you try for differentiating both sides w.r.t. x?

Answer 5

yea

Answer 6

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

Answer 7

\[\frac{d}{dx}x^2=2x \\ \frac{d}{dx}(-6xy)=-6 \frac{d}{dx}(xy)=-6(y \frac{dx}{dx} +x \frac{dy}{dx}) =-6(y+x \frac{dy}{dx}) \\ \frac{d}{dx}y^2=2y \frac{dy}{dx}\]
the differentiating part looks great
checking your algebra...

Answer 8

only complaint is that when you subtract 2x on both sides you put +2x on the right hand side

Answer 9

ooh your right

Answer 10

totally caught me off guard

Answer 11

so everything looks good except for the sign right?

Answer 12

yep

Answer 13

awesome thanks!

Answer 14

well

Answer 15

you could do a little simplifying if you wanted

Answer 16

but yeah the answer you have is right

Answer 17

3y-x/y-3x?

Answer 18

with the sign change

Answer 19

\[\frac{dy}{dx}=\frac{6y-2x}{2y-6x} =\frac{2(3y-x)}{2(y-3x)}=\frac{3y-x}{y-3x}\]

Answer 20

yup

Answer 21

but that is all you can really do