# Taylor series expansion

1. May 18, 2012

### Lizwi

how do you do the taylor series expansion of e(a+x)2

2. May 18, 2012

### chiro

Hey Lizwi and welcome to the forums.

This function is differentiable, continuous and can be expanded at any point where x is a real number.

To start off though, do you know how to differentiate your function for the nth derivative?

3. May 18, 2012

### Lizwi

Yes, I think you use the chain rule

4. May 18, 2012

### chiro

Yes you will do, but the key will be to expand your series about the point x=0 (in other words you need to find f'(0), f''(0) and so on).

If you end up getting a specific form (which you will) and then the zero's cancel out terms, then you will get a simplification for the nth derivative.

So expand out the first two or three derivatives (using the chain rule) and substitute in x = 0. What terms dissappear as a result of this?

5. May 18, 2012

### DonAntonio

Do you know the MacClaurin series for $\,e^x\,$ : $$e^x=\sum_{n=0}^\infty\frac{x^n}{n!}\,?$$ Well, you can now input $\,(a+x)^2\,$ above as this series converges for any real number...

DonAntonio