implicit differentiation
- Thread starter rileyj12
- Start date
This one is kind of laborious. Be super careful. One little mistake and it's thrown off.
Quotient rule:
\(\displaystyle 2yy'=\frac{(x^{2}+y)(1-y')-(x-y)(2x+y')}{(x^{2}+y)^{2}}\)
\(\displaystyle 2yy'(x^{2}+y)^{2}=(x^{2}+y)(1-y')-(x-y)(2x+y')\)
Do all that algebra and see if you can solve for y'.
Quotient rule:
\(\displaystyle 2yy'=\frac{(x^{2}+y)(1-y')-(x-y)(2x+y')}{(x^{2}+y)^{2}}\)
\(\displaystyle 2yy'(x^{2}+y)^{2}=(x^{2}+y)(1-y')-(x-y)(2x+y')\)
Do all that algebra and see if you can solve for y'.
mmm4444bot
Super Moderator
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- Oct 6, 2005
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Solve the equation for y` the same way that you solve an equation for any particular symbol.
Multiply out everything
Combine like-terms
Get all terms with y` to one side
Get all terms without y` to the opposite side
Factor out y`
Divide both sides by the other factor
Please show your work, if you need more help.