Will someone please explain to me how to work these differentiation logarithmic functions? :(

Question

shadowfiend · Answer

What particular issues are you having?

shadowfiend · Answer

i.e., do you have a specific problem you can show that you're having trouble with?

anonymous · Answer

Sure :D $$dy/dx=x/(1+x^2) $$ 
and I'm supposed to solve that by separating and integrating i believe, using the ln and then "e"-ing both sides to get rid of it, but I don't understand how!! 
Thank you! :)

shadowfiend · Answer

Hm. Ok, I don't have time to do the entire thing, but basically the starting point is the fact that using ln you can turn a division into a subtraction. So:

$$\ln \frac{a}{b} = \ln a - \ln b$$

You can use that to do:

$$\ln \frac{dy}{dx} = \ln \frac{x}{1 + x^2}$$
$$\ln \frac{dy}{dx} = \ln x - \ln(1 + x^2)$$

Then you can integrate the two sides. Does that help?

anonymous · Answer

Yes (: Thank you

shadowfiend · Answer

Awesome! Good to hear :)