Calculating Taylor Series for e^(x^2) around x=0

[dantheman57]

Homework Statement

Find the Taylor series of e^(x^2) about x=0

Homework Equations

Taylor Series = f(a) +f'(a)(x-a) + (f''(a)(x-a)^2)/2 ...

The Attempt at a Solution

So, the first term is pretty obvious. It's e^0^2, which is zero.

The second term is what got me. (e^x^2)'=2x*(e^x^2), so at zero that is zero. Multiply by x, still zero. But the answer key says the second term is x^2. I really cannot understand this.

Thanks!

 

[dantheman57]

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So, the first term is pretty obvious. It's e^0^2, which is zero.

My bad. e^0^2 is one. Typo.

 

[phyzguy]

Keep going. It's the f'' term that is the second term.

 

[dantheman57]

Thank you so much!

 

[micromass]

You can also take the Taylor series of e^x and then just fill in x².