# Stuff you MUST know cold for AP Calculus!

__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.

## Basic Derivatives

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## More Derivatives

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**If** a function is differentiable,

**then** it is continuous.

## Definitions
of Derivative

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##

## Differentiation Rules

Chain Rule

If _{}, then _{}.

OR

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Product Rule

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Quotient Rule

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## “PLUS A CONSTANT!”

## The Fundamental Theorem of Calculus

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where
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## 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 _{}

## 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
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