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Mathematics 19 Online
OpenStudy (fanduekisses):

Did I solve this correctly? IMPLICIT DIFFERENTIATION?

OpenStudy (jhannybean):

where's your question, lol.

OpenStudy (fanduekisses):

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

OpenStudy (misty1212):

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

OpenStudy (fanduekisses):

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

OpenStudy (fanduekisses):

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

OpenStudy (jhannybean):

There you go.

OpenStudy (misty1212):

looks good

OpenStudy (jhannybean):

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

OpenStudy (fanduekisses):

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

OpenStudy (misty1212):

i like that 1 there too, it is cute

OpenStudy (jhannybean):

Now factor our a \(y'\)

OpenStudy (fanduekisses):

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

OpenStudy (jhannybean):

Divide to isolate the \(y'\)

OpenStudy (fanduekisses):

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

OpenStudy (jhannybean):

There you go, your'e done.

OpenStudy (fanduekisses):

yay ^_^ thanks

OpenStudy (misty1212):

yay

OpenStudy (misty1212):

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

OpenStudy (misty1212):

ok just kidding

OpenStudy (fanduekisses):

lol :D

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