Mathematics 31 / 31 IB Formula Sheet
BASIC DIFFERENTIATION RULES
First Principles: If ()
y
fx then 0
()()
() lim
h
dy f x h f x
or f x
dx h
Power Rule: If n
xy then 1nn
d
x
nx
dx
Constant Rule: If ky then 0
][
dx
kd
Product Rule: If
v
uy then
ddvdu
uv u v
dx dx dx
Quotient Rule: If
v
u
y then 2
du dv
vu
du dx dx
dx v v
Chain Rule: If (),ygu where ()ufx then dy dy du
dx du dx
EXPONENTIAL & LOGARITHMIC FUNCTIONS
dx
du
ee
dx
duu
dx
du
bbb
dx
duu ln
dx
du
u
u
dx
d 1
ln 1
log ln
b
ddu
u
dx u b dx
TRIGONOMETRIC FUNCTIONS
dx
du
uu
dx
d cossin
dx
du
uuu
dx
d cotcsccsc
dx
du
uu
dx
d sincos .
dx
du
uuu
dx
d tansecsec
dx
du
uu
dx
d 2
sectan
dx
du
uu
dx
d 2
csccot
BASIC INTEGRATION RULES
Ckxdxk
1,
1
1
nC
n
x
dxx
n
n
1,
)1(
)(
)( 1
nC
na
bax
dxbax
n
n
CxwritexIf
xCxdx
x
ln0
0,ln
1
Cedxe xx
Cxdxx sincos
Cxdxx cossin
Cxdxx tansec2
Cxdxx cotcsc2
Cxdxxx sectansec
Cxdxxx csccotcsc
)1(
ln aC
a
a
dxa
x
x
