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21.
Derivative od cosh x
$\dfrac{d}{dx}\, \left( \cosh x\right) = \sinh x$
22.
Derivative od tanh
$\dfrac{d}{dx}\, \left( \tanh x\right) = \dfrac{1}{\cosh^2x}$
23.
Derivative od coth x
$\dfrac{d}{dx}\, \left( \coth x\right) = -\dfrac{1}{\sinh x}$
24.
Derivative of inverse sinh
$\dfrac{d}{dx}\, \left( \sinh^{-1} x\right) = \dfrac{1}{\sqrt{x^2+1}}$
25.
Derivative of inverse cosh
$\dfrac{d}{dx}\, \left( \cosh^{-1} x\right) = \dfrac{1}{\sqrt{x^2-1}}$
26.
Derivative od inverse tanh
$\dfrac{d}{dx}\, \left( \tanh^{-1} x\right) = \dfrac{1}{1-x^2}$
27.
Leibnitz's formula
$\left(uv\right)^{\prime\prime}=u^{\prime\prime} v + 2u^\prime v^\prime + u v^{\prime\prime}$
28.
Third derivative of a product
$\left(uv\right)^{\prime\prime\prime} = u^{\prime\prime\prime}v + 3u^{\prime\prime}v^\prime + 3u^\prime v^{\prime\prime} + 3uv^{\prime\prime\prime}$
29.
n-th derivativative of $x^m$
$\left(x^m\right)^{(n)}=\dfrac{m!}{(m-n)!}x^{m-n}$
30.
n-th derivative of $x^n$
$\left(x^n\right)^{(n)}=n!$
31.
n-th derivative of logarithm
$\left( \log_a x\right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)! }{x^n \ln x}$
32.
n-th derivative of natural logarithm
$\left(\ln x \right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)!}{x^n}$
33.
n th derivative od $a^x$
$\left(a^x\right)^{(n)}=a^x \ln^n a$
34.
$\left( a^{mx} \right)^{(n)} = m^n a^x \ln^na$
35.
n-th derivativ of sin x
$\left( \sin x \right)^{(n)} = \sin\left(x+\dfrac{n\pi}{2}\right)$
36.
n-th derivative od cos x
$\left( \cos x \right)^{(n)} = \cos\left(x+\dfrac{n\pi}{2}\right)$
37.
The constant factor rule
$\left(a \cdot f \right)' = a \cdot f'$
38.
The sum rule
$\left(f + g \right)' = f' + g'$
39.
The difference rule
$\left(f-g\right)'=f'-g'$
40.
The chain rule
$\left[ f\left(g(x)\right)\right]'=f'(g(x)) \cdot g'(x)$