If you came here looking
for advice in the stock market, you landed on a page for the wrong type of derivative. However, if you came
looking for information on the kind of derivatives used in calculus, then here you go.
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 x
^{2} + c. If I then differentiate d/dx x
^{2}
+ 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.