## Calculus: Early Transcendentals 8th Edition

$\frac{15!}{5!}=6\times 7\times 8........\times 15=10,897,286,400$
Consider the Taylor series $sinx=x-\frac{1}{3!}x^3+\frac{1}{5!}x^5-.....$ Thus, $sinx^3=x^3-\frac{1}{3!}x^9+\frac{1}{5!}x^15-.....$ $f^{15}(0)=(sin(x^{3})^{15}(0)=\frac{1}{5!}15!$ Hence, $\frac{15!}{5!}=6\times 7\times 8........\times 15=10,897,286,400$