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I differentiated the equation of kinetic energy

[tex]E(v) = \tfrac{1}{2} mv^2[/tex]

and I got:

[tex]E'(v) = mv[/tex].

I'm new to the concept of derivatives so I only know that it means that m*v is the slope of a tangent line to the graph of E at a given point.

But I can't really understand the exact meaning of it (if there are any).

Could someone explain me more about this?

Thank you