Taylor approximation involving parameter

Question

I'm have to find the order-4 Taylor approximation for $f(a)=exp(2xa-a^2)$ about $0$ where x is a parameter. I think I've gone about the right way to solve this so I'd just like to double-check. I've found the first 4 derivatives of $f(a)$ and the value of $f^{n}(0)$ for each derivative, baring in mind when I'm calculating the derivatives, I'm treating $x$ as a constant as well. So, for example, I got the first derivative of $f(a)$ as: $$f'(a)=(2x-2a)exp(2xa-a^2)$$ After that I used the taylor approximation to find the first five terms $f(x)$ with $x_0=0$. Is this the correct procedure?