Is There a Meaning Behind Leibniz's Derivative Notation?

[Jacobim]

is there an algebraic meaning to expressing the derivative of a function

as (d^2)y/(dx)^2 in the liebniz way

 

[iRaid]

$$\frac{d^{2}y}{dx^{2}}=\frac{d}{dx}(\frac{dy}{dx})$$

I think that's what you're asking?

 

[Jacobim]

yes, I see that now. Does the d^2 mean something? or just signifiy second derivative, i can see how the dx squared would be like acceleration is seconds^-2

 

[iRaid]

If you multiple the d out on top you get d²y and if you multiply the bottom you get dx²

 

[Jacobim]

but the d squared is not an exponent, its a derivative...are they the same?

 

[WannabeNewton]

They are certainly not the same; don't think of them as exponents or fractions at all it is very misleading. It is just notation to relay the fact that you have acted the operator $\frac{\mathrm{d} }{\mathrm{d} x}$ on $f$ at $x\in \mathbb{R}$ twice.