I have given a function $f$:
$ f = \begin{pmatrix} \sinh(x_1 x_2) \\ \cosh(x_1 x_2) \end{pmatrix} $
We have to show that this is possible:
$ f = \begin{pmatrix} 2x_1 x_2 \\ 1 \end{pmatrix} + \mathcal O \left( \|x\|^3 \right) $
We have used the exponential defininition of the hyperbolic function, but we always end up with terms that grow with $\sum_n \frac 1{n!}(x_1 x_2)^n$, which seem to be more than the given $\mathcal O \left( \|x\|^3 \right)$.
We are not sure how to get from $\|x\|^3$ to $x_1 x_2$. How do we attack this problem?