Question

Calculus help!
Why can't dy/dx be treated as a fraction? I can't find a counter example to why, please help.

Answer 1

dy/dx can be treated as a fraction and doing so is fairly important for certain expressions. i.e. y'=1/x then dy/dx=1/x multiplying by dx on both sides gives dy=(1/x) dx which is easily solved with integrals. What kind of problems are you working on?

Answer 2

What about the difference between differentials and derivatives? I would love to be able to safely treat dy/dx as a fraction all the time, but when it was presented that it "sometimes behaves like a fraction" my professor said that there are times when you can't treat it like a fraction and now I am doubting that and would like to use it.

I just worked out d[lnx]/dx using dx/dy = 1/(dy/dx)

Answer 3

I don't see a y in the problem, d/dx ln(x) *dx/dy = d/dy ln(x) = 0. In this case y=ln(x) then d/dx y= d/dx ln(x)=1/x=y'=dy/dx. I guess what I'm saying is that d(ln(x))/dx does not contain a y so multiplying by dx/dy does not maintain the equality of the equation.

Answer 4

no, I'm not using dy/dx to manipulate the derivative of lnx, I'm using it to find it.

Answer 5

would you mind displaying your process for getting d(ln(x))/dx=dx/dy. I tried something like that and got d(ln(x))=dy.

Answer 6

if y = lnx then x = e^y and dx/dy = e^y so that dy/dx = 1/e^y = 1/e^(lnx) = 1/x

Answer 7

That is amazing, I've never thought of it like that.