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2pie
 one year ago
find (dy/dx) by implicit differentiation (x/y)=(y/x)
2pie
 one year ago
find (dy/dx) by implicit differentiation (x/y)=(y/x)

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iambatman
 one year ago
Best ResponseYou've already chosen the best response.1dw:1381786279195:dw

iambatman
 one year ago
Best ResponseYou've already chosen the best response.1Quotient rule on both side

2pie
 one year ago
Best ResponseYou've already chosen the best response.0is it correct? what do I do next

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Multiply both sides by x^2y^2.

myininaya
 one year ago
Best 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?

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

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Distribute. 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'.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You mean equal right not plus?

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

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

2pie
 one year ago
Best ResponseYou've already chosen the best response.0\[x^2y+y^3=xy^2y^\prime + x^3 y^\prime\]

2pie
 one year ago
Best ResponseYou've already chosen the best response.0then im not sure what to do

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Factor the y' out on that one side.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[x^2y+y^3=y'(xy^2+x^3)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Divide both sides by what y' is being multiplied by.

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1You can reduce your answer.

2pie
 one year ago
Best ResponseYou've already chosen the best response.0\[x^2y+y^3/xy^2+x^3\]=\[y^\prime\]

myininaya
 one year ago
Best 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?

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

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2hey 2pie since we have x/y = y/x can we say x^2 = y^2 ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2i just did a crossmultiplication

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

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

2pie
 one year ago
Best ResponseYou've already chosen the best response.0yes by dividing 2y on both sides

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2and what would u get finally ? as dy/dx ?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1And recall from your initial equation y/x=x/y

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Now 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

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

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

2pie
 one year ago
Best ResponseYou've already chosen the best response.0thank you Im really glad I joined

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1Who couldn't pass up free math help?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2we too are glad that you joined :)
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