Unit 2: Differentiation-Limit Definition and Fundamental Properties

What is a Derivative?
What is a Derivative?
Algebra vs. Calculus
Is it Differentiable?
Derivative Notation and Language
Limit Definition of the Derivative (The Long Way)
4 Topics
Meaning: Limit Definition of the Derivative
Identifier: Limit Definition of the Derivative
Method: Limit Definition of the Derivative
Example 1: Limit Definition of the Derivative
The 5 Main Derivative Rules
5 Main Derivative Rules
Always Step 1: Simplify and Look for Algebraic Rewrites.
4 Topics
Roots or Radicals
x’s on the Bottom of a Fraction
Trig Functions Raised to a Power
Look to Make Your Life Easier
Rule 1: Constants
3 Topics
Identifier: Derivative of Constants
Method: Derivative of Constants
Example 1: Derivative of a Constant
Rule 2: Power Rule
5 Topics
Identifier: Power Rule Derivative
Method: Power Rule Derivative
Example 1: Power Rule Derivative
Example 2: Power Rule Derivative
Example 3: Power Rule Derivative
Rule 3: Product Rule
3 Topics
Identifier: Product Rule Derivative
Method: Product Rule Derivative
Example 1: Product Rule Derivative
Rule 4: Quotient Rule
3 Topics
Identifier: Quotient Rule Derivative
Method: Quotient Rule Derivative
Example 1: Quotient Rule Derivative
Rule 5: Chain Rule
3 Topics
Identifier: Chain Rule Derivative
Method: Chain Rule Derivative
Example 1: Chain Rule Derivative
Special Case Derivatives: Your new multiplication tables
Special Case Derivatives Overview
Six Trig Functions
4 Topics
Identifier: Trig Function Derivatives
Method: Trig Function Derivatives
Example 1: Trig Function Derivatives
Example 2: Trig Function Derivatives
Six Inverse Trig Functions
4 Topics
Identifier: Inverse Trig Derivatives
Method: Inverse Trig Derivatives
Example 1: Inverse Trig Derivatives
Example 2: Inverse Trig Derivatives
ex
3 Topics
Identifier: e^(x) Derivative
Method: e^(x) Derivatives
Example 1: e^(x) Derivative
ln ( x )
3 Topics
Identifier: ln(x) Derivative
Method: ln(x) Derivative
Example: ln(x) Derivative
a x = Any number raised to the x
3 Topics
Identifier: a^(x) Derivative
Method: a^(x) Derivative
Example 1: a^(x) Derivative
log b ⁡ x
3 Topics
Identifier: Logarithm Derivative
Method: Logarithm Derivative
Example 1: Logarithm Derivative
f – 1 (x) = Inverse Function
3 Topics
Identifier: Inverse Function Derivative
Method: Inverse Function Derivative
Example 1: Inverse Function Derivative
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Look to Make Your Life Easier

Unit 2: Differentiation-Limit Definition and Fundamental Properties Always Step 1: Simplify and Look for Algebraic Rewrites. Look to Make Your Life Easier

Sometimes a simple algebra move at the beginning of a math problem can change the level of difficulty dramatically.

There is no set of rules here, but just reminded yourself to stop and take a look at the problem first before you go rushing into it.

Here are just a couple of examples of what I mean. You will see that there is some personal preference in these choices.

Algebra: Look to Distribute

Less parentheses are usually better than more parentheses.

Original

Rewrite

f ( x ) = tan ( 3 π ( 2 x + 3 ) )

f ( x ) = tan ( 6 π x + 9 π )

f ( x ) = 5 x ( x 3 – 9 x + 7 )

f ( x ) = 5 x 4 – 45 x 2 + 35 x

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