A derivative is simply a type of limit, more or less?

Answer 1

A derivative is a function that provides the limit of the slope of a section of a primary function as the length of that section approaches zero.

Answer 2

The ordinary derivative is an operator that takes the limit of the slope of a line defined by two points on a function as the distance between the points approaches zero.

Answer 3

The answers I looked at don't seem to answer your question very well. A derivative is a rate of change. In physics we frequently do time derivatives like velocity (rate of change of position vs. time) and acceleration (rate of change of velocity with time).

In general you can compute of derivative with respect to any variable that a quantity depends upon, so the concept is very broad and has lots of applications.

The derivative is indeed defined as the limit of a difference quotient, but that isn't really the way to convey what it actually means.

Answer 4

Yes, the derivative is the limit to the slope of the curve

Answer 5

More or less, yes. Given a curve f(x) and a line that intercepts f(x) at two points, you could say that f'(x) is the limit, as the 2nd point approaches the first, of the slope of the secant line (which approaches tangent-hood).

Answer 6

The "derivative" of a function, a wonderful concept from calculus, separates the men from the boys (ladies from the girls?) in the sciences. This is true science, while studying "black holes" and "neutron stars" in space is just pseudo-science, pandering to the common idiom of what science is.

Here is a "black hole" or "knowledge gap" in everyday current understanding of the environment - the mass of the substance called "air". Those fluffy clouds up in the sky slowly traversing it represent hundreds of thousands of tons of mass and its kinetic energy, something foreign to almost everyone. Shakespeare in one of his sonnets complained, "And simple truth, miscalled simplicity". The modern age has a need to get with the renewables!!!!

Answer 7

the definition of derivative is a limit, yes

Answer 8

The derivative is the limit of the slope of the secant line of a curve as the change in x approaches zero, thus the tangent line to that point.

In y = f(x)
dy/dx = lim, change in x-> 0 (change in y)/(change in x)
dy/dx = lim, change in x-> 0 (y2 - y)/(change in x)
You know that
y2 = f(x2)
y = f(x)
change in x = x2 - x
x2 = x + change in x
so
dy/dx = lim, change in x -> 0 [f(x2) - f(x)]/change in x
dy/dx = lim, change in x -> 0 [f(x + change in x) - f(x)]/change in x

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