What does the derivative of the derivative tell you?

By taking the derivative of the derivative of a function f, we arrive at the second derivative, f′′. The second derivative measures the instantaneous rate of change of the first derivative. The sign of the second derivative tells us whether the slope of the tangent line to f is increasing or decreasing.

What are the two definitions of a derivative?

The definition of the derivative can be approached in two different ways. One is geometrical (as a slope of a curve) and the other one is physical (as a rate of change). Our emphasis will be on the use of the derivative as a tool.

What do derivatives actually do?

Differentiation is the action of computing a derivative. The derivative of a function y = f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to the change of the variable x. It is called the derivative of f with respect to x.

How to calculate the derivative of a function?

The derivative of a function at some point characterizes the rate of change of the function at this point. We can estimate the rate of change by calculating the ratio of change of the function Δy to the change of the independent variable Δx. In the definition of derivative, this ratio is considered in the limit as Δx → 0.

Is the derivative at the heart of calculus?

The derivative is the heart of calculus, buried inside this definition: But what does it mean? Let’s say I gave you a magic newspaper that listed the daily stock market changes for the next few years (+1% Monday, -2% Tuesday…).

Which is the defintion of the derivative of X?

Defintion of the Derivative The derivative of f (x) f (x) with respect to x is the function f ′(x) f ′ (x) and is defined as, f ′(x) = lim h→0 f (x +h)−f (x) h (2) (2) f ′ (x) = lim h → 0 f (x + h) − f (x) h

Why is the derivative is the slope of a function?

Knowing this, you can plot the past/present/future, find minimums/maximums, and therefore make better decisions. That’s pretty interesting, more than the typical “the derivative is the slope of a function” description. Let’s step away from the gnarly equation.