arthuro
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The two different notations for derivatives in math

I know that Newton and Leibniz developed the defferential and integral calculus independently at the same time, and that they used different notations for derivatives: Leibniz used, for example, dx/dt, where Newton would use x with a dot above it. Are both terms absolutely equivalent? I think I've heard something in the past that there's a slight difference between them, but I can't remember what it is.

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JGerroll
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My understanding has always been that the . relate to Newton differentiatinf with respect to time from the point of view of applied mathematics and motions of bodies.

 

This is a small subset of the application of calculus and Leibniz was looking into the mathematics of this in a 'purer' fashion - i.e. the concept of differentiating two variables.

 

Hence the notation x dot and dx/dt is equivalent in meaning but the origin is different. With the notation dx/dt it is easier to do algebra, variable substitutiion etc. and apply calculus toproblems that have nothing to do with time while at the same time explicitly stating Cartesian co-ordinates.
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Actually, to the best of my knowledge, Newton used dx/dt and Liebnitz used x dot and x dot dot (for the second derivative).  As the other answer states, x dot is more compact, but not as powerful in general.   As a result, we reserve x dot to stand for the commonly sought x dot, but we also use the more powerful (think ordinary differential equations) dx/dy dx2/dy2, etc.  It is largely because of Newton's superior notation that he is given more credit for developing Calculus
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hkabla
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Bored with knowledge? Try golf! 

Partial derivatives and multivariable functions derivative cannot be represented by x dot. dx/dt should hence be preferred, at least when the math side is to be explored.
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you can see the different in ODE ,you need to use the libniz notations to solve,

if you are use only calculus there is no diffrent.

 
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