[DRAFT] Derivative

The derivative of f at the point x is

lim(f(x+h) - f(x)) / h where lim(h->0) or

lim(f(w) - f(x)) / (w - x) where w->x.

If this limit exists, then we can say that f is differentiable at point x and the derivative is shown as f'(x)(f-prime) or d/dx f(x). The derivative is a ratio.

There is also the power rule which makes it easier to calculate derivatives.

d/dx xn = n*x^(n-1)

The sign of the derivative records how the output of the function is related to the change in the input. If the derivative is positive then if the input x increases f(x) also increases and if the derivative is negative then if the input x increases f(x) decreases. I think this is some type of correlation.