I know that the Taylor series of $f(x)$ around $a$ is given by:

$$f(x)=f(a)+f'(a)(x-a)+f''(a)\frac{(x-a)^2}{2}+\dots=\sum_{n=0}^\infty \frac{f^{(n)}(a) }{n!} (x-a)^n$$

In my textbook I see the following formula for $f(x+x')$ which I however don't understand:

$$f(x+x')=f(x)+f'(x)x' +\frac{f''(x)}{2}(x')^2+\dots=\sum_{n=0}^\infty \frac{f^{(n)}(x)}{n!} (x')^n $$

I don't understand how they obtained this formula. Can someone explain me that?