derivative and differentiation

[Brainee]

I do not understand difference between a derative and differentiation and what each means. I have searched the web but not got wiser.

[exchemist]

15 minutes ago, Brainee said:

I do not understand difference between a derative and differentiation and what each means. I have searched the web but not got wiser.

The operation of differentiation results in a derivative. d/dx (x²) represents the operation of differentiating x² and the result, 2x, is the derivative. 

[joigus]

It is possible that you mean the differential of a function.

As @exchemist said, taking the derivative and differentiating is used synonymously. But sometimes people talk about the differential, or to differentiate the variable / function, in the sense of taking small increments, and then using the derivative.

\[\Delta y = \frac{dy}{dx} \Delta x \]

https://en.wikipedia.org/wiki/Differential_(mathematics)#Introduction

Mathematicians are more rigourous, and would say that values of a function close to a given point can be expressed as a linear function of the local values of the independent variable plus a small increment:

https://en.wikipedia.org/wiki/Differential_(mathematics)#Differentials_as_linear_maps

I hope that was what you meant.

[amaila3]

I hope this explanation will help you.

Differentiation is a fundamental concept in calculus. It's the process of finding the rate at which a function changes. In simpler terms, it tells you how a quantity (usually represented as a function) is changing at a specific point. Imagine you have a function that describes the position of a car over time. Differentiation would help you determine the car's speed at a particular moment.

On the other hand, a derivative is the result of differentiation. When you perform differentiation on a function, you get another function called its derivative. This new function represents the rate of change of the original function. So, if you differentiate the position function of the car, you'll get a new function representing its speed.

In summary, differentiation is the process of finding rates of change, while a derivative is the mathematical expression or function that represents that rate of change. Think of differentiation as the action, and a derivative as the outcome.

[studiot]

37 minutes ago, amaila3 said:

I hope this explanation will help you.

Differentiation is a fundamental concept in calculus. It's the process of finding the rate at which a function changes. In simpler terms, it tells you how a quantity (usually represented as a function) is changing at a specific point. Imagine you have a function that describes the position of a car over time. Differentiation would help you determine the car's speed at a particular moment.

On the other hand, a derivative is the result of differentiation. When you perform differentiation on a function, you get another function called its derivative. This new function represents the rate of change of the original function. So, if you differentiate the position function of the car, you'll get a new function representing its speed.

In summary, differentiation is the process of finding rates of change, while a derivative is the mathematical expression or function that represents that rate of change. Think of differentiation as the action, and a derivative as the outcome.

Welcome

Nicely put. All good stuff. +1

 

Hope to see more in future.