Find the Maclaurin series for f(x)=xe3xf(x) = x e^{3x}f(x)=xe3x.
∑n=0∞3nxn+1n!\sum_{n=0}^{\infty} \frac{3^n x^{n+1}}{n!}∑n=0∞n!3nxn+1
∑n=0∞3nxnn!\sum_{n=0}^{\infty} \frac{3^n x^{n}}{n!}∑n=0∞n!3nxn
∑n=0∞3n+1xnn!\sum_{n=0}^{\infty} \frac{3^{n+1} x^n}{n!}∑n=0∞n!3n+1xn
∑n=0∞3nx2nn!\sum_{n=0}^{\infty} \frac{3^n x^{2n}}{n!}∑n=0∞n!3nx2n