nth derivative

$D^n([\sin|\cos](ax+b)) = a^n*[\sin|\cos](ax+b+n*\frac{\pi}{2})$

$D^n[(ax+b)^m] = a^n(ax+b)^{m-n}*(\frac{m!}{(m-n)!})$

$D^n[(ax+b)^{m}] = a^n(ax+b)^{m-n}*((-1)^n\frac{(-m+n-1)!}{(-m-1)!})$ if m<0

$D^n(\log(ax+b))=\frac{(-1)^{n-1}(n-1)!a^n}{(ax+b)^n}$

$D^n(e^{ax}[\sin|\cos](bx+c) = r^ne^{ax}[\sin|\cos](bx+c+n\theta)$ where $r=\sqrt{a^2+b^2}$ and $\theta=tan^{-1}\frac{b}{a}$

Product rule for nth derivative #

$$D^n(f(x)\cdot g(x)) = \sum_{r=0}^{n}(^nC_r\cdot f^{n-r}(x)\cdot g^r(x))$$