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This is an old revision of this page, as edited by Hayson1991 (talk | contribs) at 22:10, 23 October 2008 (→9). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

${\displaystyle x=\tan \left(y\right)}$

${\displaystyle 1=\sec ^{2}\left(y\right)*{\frac {dy}{dx}}}$ (Chain rule, derivative of tan=sec^2)

${\displaystyle {\frac {1}{\sec ^{2}\left(y\right)}}={\frac {dy}{dx}}}$

${\displaystyle \cos ^{2}\left(y\right)={\frac {dy}{dx}}}$

${\displaystyle {\frac {dy}{dx}}=\cos ^{2}\left(y\right)}$

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xy + xy = 6 —Preceding unsigned comment added by 74.183.242.181 (talk) 22:03, 23 October 2008 (UTC) ${\displaystyle x^{2}y+xy^{2}=6\,}$

${\displaystyle \left(2x*y+x^{2}*{\frac {dy}{dx}}\right)+\left(1*y^{2}+x*2y{\frac {dy}{dx}}\right)=0}$

${\displaystyle 2xy+x^{2}{\frac {dy}{dx}}+y^{2}+2xy{\frac {dy}{dx}}=0}$

${\displaystyle x^{2}{\frac {dy}{dx}}+2xy{\frac {dy}{dx}}=-2xy-y^{2}}$

${\displaystyle {\frac {dy}{dx}}={\frac {-2xy-y^{2}}{x^{2}+2xy}}}$

${\displaystyle {\frac {dy}{dx}}=-{\frac {2xy+y^{2}}{x^{2}+2xy}}}$