Note: Letters like a, b, c, d, m, and n are traditionally used to represent constants.
Letters like f, g, h, u, v, x, and y and traditionally used to represent variables or functions.
If a function is differentiable,
then it is continuous.
Chain Rule
If , then .
OR
Product Rule
Quotient Rule
where
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 .
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 .
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
If distance, velocity and acceleration are represented by s, v, and a, respectively, then and .
If
then