# Derivative of 14x^2: Quick Question and Solution

• Cacophony
In summary, a derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is important because it allows us to analyze how a function is changing at a specific point and has many practical applications. The derivative can be calculated using various methods and involves finding the limit of the difference quotient. It differs from an integral, which measures the accumulation of a function over a given interval. A derivative can also be negative, indicating a downward slope or decrease in the function at that point.
Cacophony

## Homework Statement

What is the derivative of 14x^2?

## The Attempt at a Solution

Do i bring the 2 in front to get 28x? Or do I use the chain rule?

Cacophony said:
Do i bring the 2 in front to get 28x? Or do I use the chain rule?

28x is the correct answer. Technically you always use the chain rule including in this case. Think about it: derivative of (14x^2) is 28x and derivative of x is 1. So by chain rule, the answer is (28x)(1) = 28x.

cool beans

## What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It can also be thought of as the slope of a tangent line to the function's graph at that point.

## Why is the derivative important?

The derivative is important because it allows us to analyze how a function is changing at a specific point. It has many applications in fields such as physics, engineering, economics, and more.

## How is a derivative calculated?

The derivative of a function can be calculated using various methods, such as the power rule, product rule, quotient rule, and chain rule. It involves finding the limit of the difference quotient as the change in the independent variable approaches zero.

## What is the difference between a derivative and an integral?

A derivative measures the rate of change of a function, while an integral measures the accumulation of that function over a given interval. In other words, a derivative tells us how a function is changing, while an integral tells us the total amount of change.

## Can a derivative be negative?

Yes, a derivative can be negative. This occurs when the slope of the tangent line is downward or when the function is decreasing at that point. In this case, the derivative represents the rate of decrease of the function at that point.

Replies
1
Views
1K
Replies
1
Views
1K
Replies
2
Views
1K
Replies
8
Views
1K
Replies
3
Views
2K
Replies
4
Views
692
Replies
7
Views
1K
Replies
4
Views
1K
Replies
23
Views
3K
Replies
3
Views
1K