Question

how to take derivatives

Answer 1

I think so that it is a decease which is very dangerous

Answer 2

Differentiation - Taking the Derivative

Differentiation is the algebraic method of finding the derivative for a function at any point. The derivative is a concept that is at the root of calculus. There are two ways of introducing this concept, the geometrical way (as the slope of a curve), and the physical way (as a rate of change). The slope of a curve translates to the rate of change when looking at real life applications. Either way, both the slope and the instantaneous rate of change are equivalent, and the function to find both of these at any point is called the derivative.

The Geometrical Concept of the Derivative

If you have ever found the slope of a line on a graph, that is the derivative. When we are looking at curves instead of linear graphs, it gets difficult to find the slope at every point, because the slopeis constantly changing. A way to find the slope is to zoom in on the graph at a point and find the slope at that point.



A way to find the slope is using the rise over run method, or the formula for slope:



The way to get a better approximated slope, or derivative, is to make the two x values as close as possible. This is a tedious process when you want to find the slope for many points on the graph. This is where differentiation comes in. The definition of a derivative comes from taking the limit of the slope formula as the two points on a function get closer and closer together.