G gopher New member Joined Jan 14, 2007 Messages 15 Feb 19, 2007 #1 ok i need to find T.L and N.L for x^3y+xy^3=30 my first step i got (3x^2*y)+(x^3*y') + (y^3)+(x*3y^2*y') = 0 is that right ? do i need to use product rule like that?
ok i need to find T.L and N.L for x^3y+xy^3=30 my first step i got (3x^2*y)+(x^3*y') + (y^3)+(x*3y^2*y') = 0 is that right ? do i need to use product rule like that?
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Feb 19, 2007 #2 Yep. \(\displaystyle \L\\x^{3}y+xy^{3}=30\) \(\displaystyle \L\\x^{3}\frac{dy}{dx}+3x^{2}y+3xy^{2}\frac{dy}{dx}+y^{3}=0\) \(\displaystyle \L\\\frac{dy}{dx}=\frac{-y^{3}-3x^{2}y}{x^{3}+3xy^{2}}\)
Yep. \(\displaystyle \L\\x^{3}y+xy^{3}=30\) \(\displaystyle \L\\x^{3}\frac{dy}{dx}+3x^{2}y+3xy^{2}\frac{dy}{dx}+y^{3}=0\) \(\displaystyle \L\\\frac{dy}{dx}=\frac{-y^{3}-3x^{2}y}{x^{3}+3xy^{2}}\)
