Summary deriv table

Rule Function Derivative Notation

Constant (c) (0) ( \frac{d}{dx}[c] = 0 )

( \frac{d}{dx}[x^n] = n
Power ( x^n ) ( n x^{n-1} )
x^{n-1} )

Constant Multi- ( c \cdot ( \frac{d}{dx}[c \cdot f(x)]
( c \cdot f(x) )
ple f'(x) ) = c \cdot f'(x) )

( f'(x) \pm ( \frac{d}{dx}[f \pm g] =
Sum/Difference ( f(x) \pm g(x) )
g'(x) ) f' \pm g' )

( f(x) \cdot ( f'(x)g(x) +
Product ( (fg)' = f'g + fg' )
g(x) ) f(x)g'(x) )

( \frac{f(x)} ( \frac{f'g - ( \left(\frac{f}{g}\right)' = \
Quotient
{g(x)} ) fg'}{g^2} ) frac{f'g - fg'}{g^2} )

( f'(g(x)) \ ( \frac{d}{dx}[f(g(x))] =
Chain ( f(g(x)) )
cdot g'(x) ) f'(g(x)) \cdot g'(x) )