Find an Expression for the General Term of the Taylor $x \sin x=x^{2}-\frac{x^{4}}{3 !}+\frac{x^{6}}{5 !}-\frac{x^{8}}{7 !}$

Multiple Choice

Find an expression for the general term of the Taylor series for $x \sin x=x^{2}-\frac{x^{4}}{3 !}+\frac{x^{6}}{5 !}-\frac{x^{8}}{7 !}$ .

A) $\frac{(-1) ^{n-1} x^{2 n-1}}{(2 n+1) !}$
B) $(-1) ^{2 n-1} \frac{x^{n+1}}{n !}$
C) $(-1) ^{n} \frac{x^{2 n+2}}{(2 n+1) !}$
D) $\frac{x^{2 n}}{2 n-1}$