Differentiation rules formulas

The constant factor rule

$\left(a \cdot f \right)' = a \cdot f'$

The sum rule

$\left(f + g \right)' = f' + g'$

The difference rule

$\left(f-g\right)'=f'-g'$

Linearity of differentiation

$\left(af+bg\right)'=af'+bg'$

The chain rule

$\left[ f\left(g(x)\right)\right]'=f'(g(x)) \cdot g'(x)$

The reciprocal rule

$\left(\dfrac{1}{f}\right)' = -\dfrac{f'}{f^2}$

The quotient rule

$\left(\dfrac{f}{g}\right)'=\dfrac{f'g-g'f}{f^2}$

Generalized power rule

$\left(f^g\right)'=f^g\,\left( f'\,\dfrac{g}{f} + g' \ln f \right)$

Logarithmic derivatives

$\left( \ln f \right)' = \dfrac{f'}{f}$