Calculus Review Sheet
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Calculus Review Sheet
ECON2010 Managerial Economics, Fall 2003, David Stern
______________________________________________________________________________
Concept of Derivatives
Marginal value of Y=f(X) is ∆Y/∆X. Derivative is the limit:
∆
limit
dY
Y
=
∆
→
∆
X
0
dX
X
Formulae for Derivatives
=
Power Rule
dY
b
Y
aX
=
−1
b
baX
dX
=
Constant
dY
0
Y
aX
= 0
dX
=
Linear
dY
1
Y
aX
=
a
dX
= ln
Natural Logarithm
dY
1
Y
X
=
dX
X
= exp
Exponential
Y
X
dY
= exp
X
dX
=
+
Sums
dY
dU
dW
Y
U X
( )
W X
( )
=
+
dX
dX
dX
=
Products
Y
UW
dY
dW
dU
=
+
U
W
dX
dX
dX
Quotients
U
dU
dW
=
−
Y
W
U
dY
W
dX
dX
=
2
dX
W
= ( ( ))
Chain Rule
dY
dY
dW
Y
f W X
=
dX
dW
dX
0 = f X Y
Implicit Function
dY
df dX
/
( , )
= −
Theorem
dX
df dY
/
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