# Thread: I don't understand differentials..dy and dx terms ect.

1. ## I don't understand differentials..dy and dx terms ect.

I know that dy/dx is the notation for the derivative of a function and i also know that dy is the infinitely small difference between two y values and dx is the infinitely small difference between two x values.

The part that confuses me is when i see the dy and dx seperated from eachother on both sides of an equation. I don't know what that means.

2. Doesn't mean much unless you are solving a separable differential equation. You can always use the rules of algebra to put them together whether you divide or multiple them across.

3. Originally Posted by jsel21
I know that dy/dx is the notation for the derivative of a function and i also know that dy is the infinitely small difference between two y values and dx is the infinitely small difference between two x values.

The part that confuses me is when i see the dy and dx seperated from eachother on both sides of an equation. I don't know what that means.
Let say we have a function such as this:

$\displaystyle \frac{dy}{dx} = \frac{F(x)}{G(y)}$.

If you treat $\displaystyle \frac{dy}{dx}$ as a simple fraction, you can "multiply" in a sense by $\displaystyle dx$ and rearrange to get.

$\displaystyle G(y)dy = F(x)dx$, and integrate both sides with respect to the respective variables.

As dwsmith said this is used when solving separable differential equations.

4. ok, another thing i don't understand is the meaning of differentiating "y in respect to x", or differentiating y in respect to any other variable. what exactly does it mean to differentiate y "in respect to" a variable?

5. Originally Posted by jsel21
ok, another thing i don't understand is the meaning of differentiating "y in respect to x", or differentiating y in respect to any other variable. what exactly does it mean to differentiate y "in respect to" a variable?
Try reading it as "as it depends on" or "as it varies with".

E.g. speed is the rate of displacement of an object with respect to (depending on) time.