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  • DLS

x^3+y^3+3axy=0 dy/dx=?

Mathematics
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  • DLS
\[\LARGE 3x^{2}+3y^{2} \frac{dy}{dx}-3ax=0\] this gives..finally.. \[\LARGE \frac{dy}{dx}=\frac{x(a-x)}{y^{2}} \] I doubt this because im quite unsure about the derivative of 3axy,we are differentiating wrt x or y? if its x then 3ay(dx//dx) not sure..
  • DLS
you'll need product rule for 3axy

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Other answers:

  • DLS
I thought product rule was used for function times function
  • DLS
thats a variable,isn't it
y is the function of x, x is the function of x.
  • DLS
:O
(xy)' = x'y+xy' = y+xy'
  • DLS
so how will we find for 3axy?
3a (y+xy')
  • DLS
\[\LARGE 3ay(\frac{dx}{dx}) |||| 3ax(\frac {dy}{dx}) \]
dx/dx=1
  • DLS
yeah!
and i assume ||| is +
  • DLS
yes
  • DLS
thats it?:O
so, dy/dx will change..
  • DLS
what do u mean?
i mean recalculate dy/dx
  • DLS
\[\LARGE \frac{dy}{dx}= \frac{-3(ay+x^{2})}{3(y^{2}-ax)} \]
-ax ?
  • DLS
sorry + printing mistake :P
then ok.
  • DLS
:D

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