Derivative Help: Understanding x2+x

[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 nx^n-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.

 

[Duncan1382]

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 nx^n-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.

 

[bns1201]

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

 

[schlynn]

Thank you so much.