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221.
Derivative of inverse cosh
$\dfrac{d}{dx}\, \left( \cosh^{-1} x\right) = \dfrac{1}{\sqrt{x^2-1}}$
222.
Derivative od inverse tanh
$\dfrac{d}{dx}\, \left( \tanh^{-1} x\right) = \dfrac{1}{1-x^2}$
223.
Leibnitz's formula
$\left(uv\right)^{\prime\prime}=u^{\prime\prime} v + 2u^\prime v^\prime + u v^{\prime\prime}$
224.
Third derivative of a product
$\left(uv\right)^{\prime\prime\prime} = u^{\prime\prime\prime}v + 3u^{\prime\prime}v^\prime + 3u^\prime v^{\prime\prime} + 3uv^{\prime\prime\prime}$
225.
n-th derivativative of $x^m$
$\left(x^m\right)^{(n)}=\dfrac{m!}{(m-n)!}x^{m-n}$
226.
n-th derivative of $x^n$
$\left(x^n\right)^{(n)}=n!$
227.
n-th derivative of logarithm
$\left( \log_a x\right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)! }{x^n \ln x}$
228.
n-th derivative of natural logarithm
$\left(\ln x \right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)!}{x^n}$
229.
n th derivative od $a^x$
$\left(a^x\right)^{(n)}=a^x \ln^n a$
230.
$\left( a^{mx} \right)^{(n)} = m^n a^x \ln^na$
231.
n-th derivativ of sin x
$\left( \sin x \right)^{(n)} = \sin\left(x+\dfrac{n\pi}{2}\right)$
232.
n-th derivative od cos x
$\left( \cos x \right)^{(n)} = \cos\left(x+\dfrac{n\pi}{2}\right)$
233.
The constant factor rule
$\left(a \cdot f \right)' = a \cdot f'$
234.
The sum rule
$\left(f + g \right)' = f' + g'$
235.
The difference rule
$\left(f-g\right)'=f'-g'$
236.
The chain rule
$\left[ f\left(g(x)\right)\right]'=f'(g(x)) \cdot g'(x)$
237.
The reciprocal rule
$\left(\dfrac{1}{f}\right)' = -\dfrac{f'}{f^2}$
238.
The quotient rule
$\left(\dfrac{f}{g}\right)'=\dfrac{f'g-g'f}{f^2}$
239.
Generalized power rule
$\left(f^g\right)'=f^g\,\left( f'\,\dfrac{g}{f} + g' \ln f \right)$
240.
Logarithmic derivatives
$\left( \ln f \right)' = \dfrac{f'}{f}$