Derivatives in Calculus
There are of course an infinite number of derivatives, but the ones I have listed here are some of the most common. The derivative is basically the dual of the integral. Integrating the derivative of a function yields a scaled version of the original function. To be mathematically correct, it is necessary to add an unknown constant to the integrated result form because it evaluates to zero when the derivative is taken.
Sound confusing? It really isn't. If I integrate the function ∫ x dx, the answer is x2 + c. If I then differentiate d/dx x2 + c, I get x/2 + 0. So, the scaling factor is 1/2 in this case; it could be 1 or anything else depending on the function.