# Need a list on derivatives in Physics

#### Noone1982

For a school project, I am trying to compile a good sized list of the interelation of derivatives in physics. I know I can just go through every page in my book but does anyone know any handy links off hand?

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#### vanesch

Staff Emeritus
Gold Member
You mean, the derivative of a function, as in calculus ?

If it's that, know that the mathematical concept of derivative was essentially invented to express a certain concept in physics: "change". Newton and Leibniz are considered to be its inventors.
"change of position with time" = velocity
Newton needed to write down velocity as a function of time, when he had position as a function of time. Hence his definition of velocity v = dx /dt

"change of velocity with time" = acceleration, a = dv/dt = d^2 x/dt^2

Acceleration is the second derivative wrt time, of position.

Newton needed that, to write his famous law: mass x acceleration = force

But the concept of derivative got also used in other ways. For instance, the ELECTRIC FIELD is (minus) the change of potential with position:
E_x = - dV/dx

Note that we now have a derivative towards space, not towards time. So the derivative concept is used further than just "change in time".

In modern physics, derivatives abound, in many ways...