Question

Did I solve this correctly? IMPLICIT DIFFERENTIATION?

Answer 1

where's your question, lol.

Answer 2

If \[if~~x^2+xy+y^3=0,~then~~~\frac{ dy }{ dx }=?\]

Answer 3

just a suggestion, but it is usually easier to write \(y'\) instead of all those \(\frac{dy}{dx}\)'s

Answer 4

\[2x+[1*y+x*\frac{ dy }{ dx }]+3y^2*\frac{ dy }{ dx }=0\]

Answer 5

\[2x+y+x*y'+3y^2*y'=0\]

Answer 6

There you go.

Answer 7

looks good

Answer 8

So send all the stuff that doesn't have a \(y'\) to the other side of the equation.

Answer 9

\[xy'+3y^2y'=-2x-y\]

Answer 10

i like that 1 there too, it is cute

Answer 11

Now factor our a \(y'\)

Answer 12

\[y'(x+3y^2)=-2x-y\]

Answer 13

Divide to isolate the \(y'\)

Answer 14

\[y'=\frac{ -2x-y }{ x+3y^2 }\]

Answer 15

There you go, your'e done.

Answer 16

yay ^_^ thanks

Answer 17

yay

Answer 18

now go ahead and find \(y''\)

Answer 19

ok just kidding

Answer 20

lol :D