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1.
The constant factor rule
$\left(a \cdot f \right)' = a \cdot f'$
4.
The chain rule
$\left[ f\left(g(x)\right)\right]'=f'(g(x)) \cdot g'(x)$
5.
The reciprocal rule
$\left(\dfrac{1}{f}\right)' = -\dfrac{f'}{f^2}$
6.
The quotient rule
$\left(\dfrac{f}{g}\right)'=\dfrac{f'g-g'f}{f^2}$
7.
Generalized power rule
$\left(f^g\right)'=f^g\,\left( f'\,\dfrac{g}{f} + g' \ln f \right)$
8.
Logarithmic derivatives
$\left( \ln f \right)' = \dfrac{f'}{f}$
9.
The chain rule - general formula for composite functions
$\left(f\left(g(x)\right)\right)'=f'(g(x))\cdot g'(x)$