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iambatmanBest ResponseYou've already chosen the best response.1
dw:1381786279195:dw
 6 months ago

iambatmanBest ResponseYou've already chosen the best response.1
Quotient rule on both side
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
is it correct? what do I do next
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[\frac{yxy'}{y^2}=\frac{xy'y}{x^2}\] I would clear the fractions first.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Multiply both sides by x^2y^2.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[x^2y^2 \frac{yxy'}{y^2}=x^2y^2\frac{xy'y}{x^2}\] You see that we can write this without the fractional style now, right?
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
yes by calcelling the \[y ^{2} x^{2}\] on each side respectively \[x^{2}(yxy^1)+y^2(xy^1y)\] then?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Distribute. Put y' terms on one side and the other nony' terms on the other side Then factor y' out. The divide by whatever is being multiplied by y'.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
You mean equal right not plus?
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
After I multiply I got\[x^2yx^3y^\prime =xy^2y^\primey^3\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Right. Continue. Put y' terms together on one side and then nony' terms on the other.
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
\[x^2y+y^3=xy^2y^\prime + x^3 y^\prime\]
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
then im not sure what to do
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Factor the y' out on that one side.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[x^2y+y^3=y'(xy^2+x^3)\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Divide both sides by what y' is being multiplied by.
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
You can reduce your answer.
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
\[x^2y+y^3/xy^2+x^3\]=\[y^\prime\]
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
\[y'=\frac{x^2y+y^3}{xy^2+x^3} =\frac{y(x^2+y^2)}{x(y^2+x^2)}\] Anything cancel?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Now instead of starting the way you guys did at the beginning. I think @hartnn would like to show you a easier way.
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
hey 2pie since we have x/y = y/x can we say x^2 = y^2 ?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
i just did a crossmultiplication
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
I think the slope can be simplified even more by the way when you guys are done. :)
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
and then we can differentiate x^2=y^2 to get 2x =2y dy/dx can you isolaye dy/dx from this ?
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
yes by dividing 2y on both sides
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
and what would u get finally ? as dy/dx ?
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
And recall from your initial equation y/x=x/y
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Now another way... x^2=y^2 or x^2y^2=0 or (xy)(x+y)=0 or xy=0 or x+y=0 or y=x or y=x If y=x, then y'=1 If y=x, then y'=1
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
wow it was easier than I thought thank you very much for your help and time @myininaya @hartnn :)
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
i see you are new here , so \[ \begin{array}l\color{red}{\text{W}}\color{orange}{\text{e}}\color{#e6e600}{\text{l}}\color{green}{\text{c}}\color{blue}{\text{o}}\color{purple}{\text{m}}\color{purple}{\text{e}}\color{red}{\text{ }}\color{orange}{\text{t}}\color{#e6e600}{\text{o}}\color{green}{\text{ }}\color{blue}{\text{O}}\color{purple}{\text{p}}\color{purple}{\text{e}}\color{red}{\text{n}}\color{orange}{\text{S}}\color{#e6e600}{\text{t}}\color{green}{\text{u}}\color{blue}{\text{d}}\color{purple}{\text{y}}\color{purple}{\text{!}}\color{red}{\text{!}}\color{orange}{\text{ }}\color{#e6e600}{\text{:}}\color{green}{\text{)}}\color{blue}{\text{}}\end{array} \]
 6 months ago

2pieBest ResponseYou've already chosen the best response.0
thank you Im really glad I joined
 6 months ago

myininayaBest ResponseYou've already chosen the best response.1
Who couldn't pass up free math help?
 6 months ago

hartnnBest ResponseYou've already chosen the best response.2
we too are glad that you joined :)
 6 months ago
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