Summary of Basic Derivative Rules
Common Functions
Constant
Square
Function
c
x
x2
Square Root
x
Exponential
ex
ax
Logarithms
ln(x)
loga(x)
Trigonometry (x is in radians)
sin(x)
cos(x)
tan(x)
cot(x)
sec(x)
csc(x)
Inverse Trigonometry
sin-1(x)
cos-1(x)
tan-1(x)
Rules
Multiplication by constant
Power Rule
Sum Rule
Difference Rule
Product Rule
Quotient Rule
Reciprocal Rule
Chain Rule
(as "Composition of Functions")
Chain Rule (in a different form)
Function
cf
xr
f+g
f-g
fg
f
g
1
f
Derivative
0
1
2x
½x-½
ex
ax (ln a)
1
x
1
x ln( a )
cos(x)
-sin(x)
sec2(x)
-csc2(x)
sec(x) tan(x)
-csc(x) cot(x)
1

1  x2
1
1  x2
1
1  x2
Derivative
cf’
rxr-1
f’ + g’
f’ - g’
f g’ + f’ g
f ' g  g' f
g2

f'
f2
fºg
(f’ º g) × g’
f(g(x))
f’(g(x))g’(x)