Table of Higher Order Derivatives.

$(x^{p})^{(n)} = p (p - 1) (p - 2) . . . (p - n + 1) x^{p - n} .$

$(a^{x})^{(n)} = a^{x} \ln^{n} a (e^{x})^{(n)} = e^{x}$

$(\sin α x)^{(n)} = α^{n} \sin (α x + \frac{π n}{2})$

$(\cos α x)^{(n)} = α^{n} \cos (α x + \frac{π n}{2})$

${((a x + b)^{p})}^{(n)} = a^{n} p (p - 1) (p - 2) . . . (p - n + 1) (a x + b)^{p - n}$

$(\log_{a} | x |)^{(n)} = \frac{(- 1)^{n - 1} (n - 1)!}{x^{n} \ln a}$

$(\ln | x |)^{(n)} = \frac{(- 1)^{n - 1} (n - 1)!}{x^{n}}$

$(α u (x) + β v (x))^{(n)} = α u^{(n)} (x) + β v^{(n)} (x)$

$(u (x) v (x))^{(n)} = \sum_{k = 0}^{n} C_{n}^{k} u^{(k)} (x) v^{(n - k)} (x), где C_{n}^{k} = \frac{n!}{k! (n - k)!}$

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