So,I found a problem where I have to evaluate the fifth derivative evaluated on $\ x=1 $, and the tenth derivative on $\ x=0 $ for the following function:
$\ f(x)=(x^2-3x)e^{x^4} $
I am supposed to find those two specific derivatives by using Taylor series.
I assume it wants me to use the taylor series for $\ e^x $ ,where, if I am correct:
$$e^{x^4}=1+\frac{1}{1!}(x^{4})+\frac{1}{2!}(x^{4})^2+\frac{1}{3!}(x^{4})^3+\frac{1}{4!}(x^{4})^4+\ldots $$
But I do not know how to continue, or what to do with the rest of the terms, in short, I am clueless!