Given that sin(x)=x−x33!+x55!−⋯\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdotssin(x)=x−3!x3+5!x5−⋯, what is the Maclaurin series for f(x)=xsin(x)f(x) = x\sin(x)f(x)=xsin(x)?
x2−x46+x6120−⋯x^2 - \frac{x^4}{6} + \frac{x^6}{120} - \cdotsx2−6x4+120x6−⋯
x−x36+x5120−⋯x - \frac{x^3}{6} + \frac{x^5}{120} - \cdotsx−6x3+120x5−⋯
x2+x46+x6120+⋯x^2 + \frac{x^4}{6} + \frac{x^6}{120} + \cdotsx2+6x4+120x6+⋯
x+x2−x32+⋯x + x^2 - \frac{x^3}{2} + \cdotsx+x2−2x3+⋯