The Tangent Line The Secant Line. The Tangent Line The Secant Line.

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Presentation transcript:

The Tangent Line The Secant Line

The Tangent Line The Secant Line

The Tangent Line The Secant Line

Use the Definiton of the Derivative to find f’(x) if

Definiton of the Derivative Examples

f(x) is after minus sign, or better yet, set h=0

Definiton of the Derivative Examples f(x) is after minus sign, or better yet, set h=0

Definiton of the Derivative Examples f(x) is after minus sign, or better yet, set h=0

Definiton of the Derivative Examples f(x) is after minus sign, or better yet, set h=0

You finish the rest! Row 0 Row 1 Row 2 Row 3

 Expand: F.O.I.L Where do you see this in Pascal’s Triangle? Combine Like Terms ROW 3 Pencils Down

 Use Pascal’s Triangle to expand: 4 th Row

 Your Turn: 6 th Row

Use the Definiton of the Derivative to find f’(x) if

Prove that if

Power Rule I…

Derive the derivative if

Evaluate the Difference Quotient if

Power Rule I…

Power Rule II…

Derive the derivative of the function:

Power Rule I…

Power Rule II…

Logs and Exponentials…

Trigonometry…

Derive the Sum Rule for Derivatives:

Derive the constant rule for derivatives:

Definitions, Rules & Theorems

Derive the derivative of the function:

Product Rule Ex 1) Find f’(x)

Product Rule Ex 2) Find f’(x)

Product Rule Ex 3) Find f’(x)

Product Rule Ex 4) Find f’(x)

Product Rule Ex 5) Find f’(x)

Product Rule Ex 6) Find f’(x)

Derive the derivative of the function:

Ex 1) Find f’(x) Quotient Rule

Ex 2) Find f’(x) Quotient Rule

Ex 3) Find f’(x) Quotient Rule

Ex 4) Find f’(x) Quotient Rule

Ex 5) Find f’(x) Quotient Rule

Ex 5) continued Quotient Rule

Ex 6) Find f’(x) Quotient Rule

Ex 6) continued Quotient Rule

Ex 7) Find f’(x) Quotient Rule

Ex 7) continued Quotient Rule

Ex 8) Find f’(x) Quotient Rule

Ex 8) continued Quotient Rule