THE CHAIN RULE
LT 3: I can find and evaluate
derivatives of functions.
ST 3.3: I can find derivatives by applying the Chain
Rule.
The Chain Rule
Example
For each function, find the
composite parts:
Practice
For each function, find the
composite parts:
Exa
PRODUCT + QUOTIENT
RULES & HIGHERORDER DERIVATIVES
LT 3: I can find and evaluate
derivatives of functions.
ST 3.2: I can find derivatives by applying basic
differentiation rules.
The Product Rule
Example:
Find:
&
Practice
Find the derivative of:
Example
F
CONTINUITY &
ONE-SIDED LIMITS
LT 2: I can find and evaluate limits of
functions.
ST 2.3: I can determine the continuity of functions
and determine one-sided limits.
Continuity
Continuous =
Not Continuous
Definition of Continuous
Discontinuities
Discontinu
DERIVATIVE & THE
TANGENT LINE
LT 3: I can find and evaluate
derivatives of functions.
ST 3.1: I can find derivatives and slopes using limits.
Review Tangent + Secant
Lines
Tangent line =
Secant line =
Tangent & the Slope
To find the tangent at a particula
RELATED RATES
LT 3: I can find and evaluate
derivatives of functions.
ST 3.6: I can apply my knowledge of derivatives
to find related rates.
Related Rates
Imagine this cone
is leaking water.
The rate at which
is drains depends
on two variables:
height and
BASIC
DIFFERENTIATION &
RATES OF CHANGE
LT 3: I can find and evaluate
derivatives of functions.
ST 3.2: I can find derivatives by applying basic
differentiation rules.
The Constant Rule
Example
Find the derivatives of each of the
following functions:
The
Grapple
How might the derivative of a
function help us identify if the graph
is increasing or decreasing?
INCREASING &
DECREASING
FUNCTIONS
LT 1: I can apply my knowledge of
differentiation to a variety of situations.
ST 1.3: I can identify intervals of i
IMPLICIT
DIFFERENTIATION
LT 3: I can find and evaluate
derivatives of functions.
ST 3.4: I can find derivatives through implicit
differentiation.
Implicit v. Explicit Functions
Implicit =
Explicit =
Examples:
Implicit v. Explicit Functions
Often we can di