Math For Economics Formula Sheet - The Economics Network
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1
2y
–
y
m
=
(x
, y
)
2
1
x
–
x
1
1
2
1
Differentiation
Graphs of Common Functions
dy
y = mx + c; m = gradient; c = vertical intercept
y = f(x)
= f’(x)
Studying
Economics
Studying Economics
dx
Linear
y
–
y
k, constant
0
m
=
2
1
x
–
x
(x
, y
)
(x
, y
)
x
1
2
1
2
2
1
1
2x
x
2
y
–
y
(x
, y
)
3x
m
=
x
2
1
(x
, y
)
3
2
2
2
x
–
x
1
1
2
1
, any constant n
x
nx
n
n–1
e
e
= y
x
x
e
ke
= ky
kx
kx
y
–
y
m
=
2
1
e
f’(x)e
f (x)
e ≈ 2.7183 is the exponential constant
Exponential functions
f(x)
x
–
x
(x
, y
)
2
1
ln x
1/x
1
1
ln kx = log
1/x
kx
d
d
u
d
v
d
d
d
u
v
e
(x
, y
)
(
u
(
x
)
v
(
x
))
=
(
(
)
(
))
u
x
v
x
=
d
x
d
x
d
x
ln f(x)
d
d
d
2
2
x
f’(x)/f(x)
x
x
±
±
±
±
d
d
d
u
v
(
(
)
(
))
u
x
v
x
=
d
d
d
x
x
x
d
d
u
d
v
d
d
f
±
d
±
d
f
(
u
(
x
)
v
(
(
x
))
=
(
))
k
f
x
=
k
(
k
f
(
x
))
=
k
d
x
d
d
x
d
x
d
x
x
d
x
d
x
±
±
d
The sum–difference rule
d
d
d
Constant multiples
d
f
u
v
(
u
(
x
)
v
(
x
))
=
(
k
f
(
x
))
=
k
d
d
d
d
x
d
x
x
x
x
d
d
f
±
±
d
d
d
v
u
d
for k constant
d
d
(
(
))
v
u
k
f
x
=
k
(
uv
)
=
u
+
v
(
)
uv
=
u
+
v
Graph of y = e
showing
Graph of y = e
showing
d
d
x
x
x
–x
d
d
d
x
x
x
d
d
d
x
x
x
d
d
f
d
d
d
exponential growth
exponential decay
v
u
(
(
))
k
f
x
=
k
(
)
uv
=
u
+
v
d
d
x
x
d
d
d
x
x
x
d
d
The product rule
u
v
The quotient rule
d
d
d
d
v
d
u
u
v
v
–
u
v
–
u
(
uv
)
=
u
+
v
d
u
d
d
d
u
x
x
d
x
d
x
d
x
d
x
d
x
=
y = ax
+ bx + c
Maths for
=
2
d
d
u
v
d
x
v
d
d
d
v
d
x
v
v
u
2
v
2
v
–
u
(
uv
)
=
u
+
v
d
u
d
x
d
x
Quadratic functions
d
d
d
x
x
x
=
d
d
u
v
d
v
–
u
x
v
v
2
d
d
d
d
u
y
y
u
d
d
d
d
d
y
y
u
The chain rule
x
x
.
If
=
(
, )
where
, )
then
.
y
=
y
u
u
=
u
(
x
If
(
=
, )
where
, )
then
y
=
y
u
u
=
u
(
x
=
d
d
d
x
v
u
v
d
d
d
v
x
u
x
d
d
d
2
x
u
x
Economics
v
–
u
d
d
d
d
y
y
u
u
d
d
x
x
.
If
(
, )
where
, )
then
=
y
=
y
u
u
=
u
(
x
=
d
d
d
d
x
v
x
u
x
v
2
d
d
d
y
y
u
.
If
(
, )
where
, )
then
y
=
y
u
u
=
u
(
x
=
Integration
d
d
d
x
u
x
d
d
d
y
y
u
f
(
x
)
f
(
x
)
d
x
.
PRINCIPLES AND FORMULAE
If
(
, )
where
, )
then
y
=
y
u
u
=
u
(
x
=
d
d
d
x
u
x
∫
k, (any) constant c
k
x
+
c
(1) b
– 4ac < 0;
(2) b
– 4ac = 0;
(3) b
– 4ac > 0
2
2
2
x
2
x
+
c
2
x
3
x
2
+
c
TC = a + bq – cq
+ dq
y = a/x = ax
Total cost functions
Inverse functions
2
3
–1
3
x
n+1
x , (n = –1)
n
+
c
A lifeline for economics students
n+1
x = 1/x
ln x + c
–1
e
e
+
c
q = a/p = ap
–1
x
x
e
kx
Economics
e
+
c
kx
Network
k
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