Basic Derivatives
More Derivatives
If a function is differentiable,
then it is continuous.
Definitions
of Derivative
Differentiation Rules
Chain Rule
If 
, then 
.
OR
Product Rule
Quotient Rule
“PLUS A CONSTANT!”
The Fundamental Theorem of Calculus
where
Corollary to the FTC
Intermediate Value Theorem
If function f is continuous for all x in the closed interval
, and y is a number
between 
and 
, then there is a number 
in 
for which 
.
Rolle’s Theorem
If f
is differentiable for all values of x
in the open interval , and f is continuous at 
and at 
, and 
,
then
there is at least one number in such that 
.
Mean Value Theorem
If f is differentiable for all values of x in the open interval , and f is
continuous at 
and 
, then there is at least one number 
in such that 
Trapezoidal Rule
Distance, Velocity, and Acceleration
If distance, velocity and
acceleration are represented by s, v, and a, respectively, then 
and 
.
l'Hôpital’s Rule
If 
then
