# Derivative Help: Understanding x2+x

• schlynn
In summary, you need to know the rules of derivatives in order to solve a homework equation. You also need to know what n is and where it comes from. You need to be able to find the derivative of a function at a certain point using the derivative formula.
schlynn

## Homework Statement

Ok, I am learning about derivative's, and they seem to elude me for some reason. I have this.

x2+x

I know the derivative is 5, and the function is differentiable at 2. But I don't understand how you get it. I know the limit you use to find it, but the shortcut is nxn-1 right? Where does n come from? And x=2 right? Would it be 2*21? But that's not 5, its 4. What am I doing wrong? Please, detailed answers are very very appreciated.

## Homework Equations

Pretty sure that I noted all the nessicary equations above.

## The Attempt at a Solution

I said what I attempted above.

schlynn said:

## Homework Statement

Ok, I am learning about derivative's, and they seem to elude me for some reason. I have this.

x2+x

I know the derivative is 5, and the function is differentiable at 2. But I don't understand how you get it. I know the limit you use to find it, but the shortcut is nxn-1 right? Where does n come from? And x=2 right? Would it be 2*21? But that's not 5, its 4. What am I doing wrong? Please, detailed answers are very very appreciated.

## Homework Equations

Pretty sure that I noted all the nessicary equations above.

## The Attempt at a Solution

I said what I attempted above.
You've just got to learn the rules of derivatives.

The derivative is:

f(x) = 2x + 1

for the first one, pull out the exponent and make it a coefficient while lowering the exponent by 1 degree. Same thing for the second term.

The original function x^2+x can be seen as x^2+x^1

n is the exponent for each x, so for the first x, n=2 and n=1 for the second x

then use the derivative formula which is dy/dk of f(x) = nx^(n-1)

which would mean the derivative is 2x^(2-1)+1x^(1-1) which equates to 2x^2+1

since it asks what the value of dy/dx is at x=2, you plug 2 into the derivative for an answer of 2(2)+1 which equals 5

Thank you so much.

## What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function with respect to its input variable. In simpler terms, it describes how much a function is changing at a specific point.

## How do you find the derivative of x2+x?

The derivative of x2+x is 2x+1. This can be found by using the power rule, which states that the derivative of xn is nx^(n-1), and the constant multiple rule, which states that the derivative of cx is c times the derivative of x.

## Why is understanding derivatives important?

Understanding derivatives is important because they are used in many areas of science and mathematics, including physics, engineering, economics, and statistics. They allow us to analyze how variables are related and make predictions about how they will change.

## What is the purpose of the x2 term in the function x2+x?

The x2 term is a polynomial term that represents the squared value of the input variable. In the context of derivatives, it allows us to analyze the curvature of a function and determine if it is increasing or decreasing at a specific point.

## Can derivatives be negative?

Yes, derivatives can be negative. A negative derivative indicates that the function is decreasing at a specific point, while a positive derivative indicates that the function is increasing at a specific point. Zero derivatives indicate a horizontal tangent line.

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