A community for students.
Here's the question you clicked on:
 0 viewing
2pie
 2 years ago
find (dy/dx) by implicit differentiation (x/y)=(y/x)
2pie
 2 years ago
find (dy/dx) by implicit differentiation (x/y)=(y/x)

This Question is Open

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

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

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

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

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

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

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

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

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

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

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

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

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

myininaya
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.2i just did a crossmultiplication

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

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

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

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

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2we too are glad that you joined :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.