find the finite expansion of $f$ to order $2$ in neighborhood of $0$

Question

find the finite expansion of $f$ to order $2$ in the neighborhood of $0$

$$f_(x)=\big(2e^x-\cosh(x\sqrt{2})\big)^{\left(\frac {1}{\sinh x}\right)}$$

Answer 1

$$f(x)=(2e^x-\cosh(\sqrt2x))^{1/\sinh x}=e^{2}-2e^{2}x+\frac{14}{3}e^{2}x^2+o\left(x^2\right)$$