What is the Maclaurin series for f(x)=sin(x)cos(x)f(x) = \sin(x) \cos(x)f(x)=sin(x)cos(x)?
∑n=0∞(−1)n22nx2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n} x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(−1)n22nx2n+1
∑n=0∞(−1)n22nx2n+1(2n)!\sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n} x^{2n+1}}{(2n)!}∑n=0∞(2n)!(−1)n22nx2n+1
∑n=0∞(−1)n22n+1x2n+1(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n+1} x^{2n+1}}{(2n+1)!}∑n=0∞(2n+1)!(−1)n22n+1x2n+1
∑n=0∞(−1)n22nx2n+12(2n+1)!\sum_{n=0}^{\infty} \frac{(-1)^n 2^{2n} x^{2n+1}}{2(2n+1)!}∑n=0∞2(2n+1)!(−1)n22nx2n+1