The $43$rd derivative of $\sin(x^{13}+x^{15})$ | Calculus 1 A question from a test of my professor on calculus 1:
Find the $43$rd derivative of $\sin(x^{13}+x^{15})$ at $x=0$.
Any idea I had didn't work, BTW, good luck to me on the test next week :X

Expand $\sin(x)$ around zero to get:
$$\sin(x)\sim x-\frac{x^3}{6}$$
$$\sin(x^{13}+x^{15})\sim x^{13}+x^{15}-\frac{x^{39}}{6}-\frac{x^{41}}{2}-\frac{x^{43}}{2}-\frac{x^{45}}{6}+O\left(x^{46}\right)$$
Take the $43$'rd derivative to get:
$$-43!/2$$
