# X^2 relation to 2x, 2x+1

1. Dec 4, 2015

### jaja1990

Is there a relation between the fact that the derivative of x^2 is 2x and that the difference between 1,4,9,16, ... is 3, 5, 7, 9, ...?

And why is the difference always 2?

2. Dec 4, 2015

### Samy_A

$(x+1)²-x²=2x+1$

This shows why the difference is always 2.

3. Dec 4, 2015

### PeroK

If you spotted that you should look for a pattern in the sequence $x^3: 1, 8, 27, 64 \dots$