Please help
the equation of the curve is
x lny = 2x + 1

the question asks to show that dy/dx = -y/x^2

i only got as far as :
lny + x/y dy/dx = 2

now what ?
thank you :D

Question

Please help
the equation of the curve is 
x lny = 2x + 1

the question asks to show that dy/dx = -y/x^2

i only got as far as : 
lny + x/y dy/dx = 2 

now what ? 
thank you :D

geerky42 · Answer

Try divide both sides by x then take the derivative.

geerky42 · Answer

$$x \ln y = 2x + 1 \Rightarrow \ln y = \dfrac{2x + 1}{x}$$
$$\dfrac{\text{d}}{\text{d}x}\ln y = \dfrac{\text{d}}{\text{d}x}\left(\dfrac{2x + 1}{x} \right)  $$
$$\dfrac{1}{y} \cdot \dfrac{\text{d}y}{\text{d}x} = \dfrac{\text{d}}{\text{d}x}\left(\dfrac{2x + 1}{x} \right) $$

anonymous · Answer

if i divide both sides by x i get 
1/y dy/dx = 2/x - 2x -1

anonymous · Answer

ok so how do i get that to equal

nubeer · Answer

try looking at the steps @geerky42  have done..
your question is this. x lny = 2x + 1
just divide both sides by x

geerky42 · Answer

Maybe it won't work. All you have to do is to make equation clean and simple. From that, you probably will find a way to prove that dy/dx = -y/x².

geerky42 · Answer

Make it simple, then take the derivative of it then simplify it.

nubeer · Answer

hmm @geerky42  are u saying your method won't work the one u have mentioned or what?

geerky42 · Answer

I don't know. Try it and figure it out.

nubeer · Answer

it would work i have tried it..

geerky42 · Answer

If it doesn't work, find another way to approach to solution.

anonymous · Answer

nubeer you got -y/x^2 ?

nubeer · Answer

yup.. @geerky42  approach of solving the question is right.. just keep simplifying same way he has done.

geerky42 · Answer

Ok. Thanks. 

Do you know what to do now? @1234abdc

anonymous · Answer

no, I'm really confused

geerky42 · Answer

Just divide both sides by x so you won't have ugly and scary-look equation when you derivative it.

geerky42 · Answer

Do you know how to take the derivative, right?

anonymous · Answer

yes i do. my problem is simplifying

geerky42 · Answer

Well, can you do it from here?

anonymous · Answer

$$\frac{ 1 }{ y } \frac{ dy }{ dx } = \frac{ 2 }{ x } - 2x - 1$$

anonymous · Answer

now what ?

geerky42 · Answer

None, it's not correct. Do you know quotient rule, right?

anonymous · Answer

yes.. why is it wrong ?

geerky42 · Answer

I don't know how you got $ \dfrac{2}{x}-2x-1 $, but I got $ \dfrac{2x - (2x+1)}{x^2}  $ which can be simplifed to $ -\dfrac{1}{x^2} $.

anonymous · Answer

oh ! i just got it
i made a really stupid mistake 
thank you for your help :D

geerky42 · Answer

You're welcome. Glad I helped.

help!!!! · Answer

agreed