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Proof - The Derivative of Secant: d/dx[sec(x)]

Proof - The Derivative of Secant: d/dx[sec(x)]

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Proof - The Derivative of Cotangent: d/dx[cot(x)]

Proof - The Derivative of Cotangent: d/dx[cot(x)]

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Proof - The Derivative of Tangent: d/dx[tan(x)]

Proof - The Derivative of Tangent: d/dx[tan(x)]

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Proof - The Derivative of f(x)=a^x: d/dx[a^x]=(ln a)a^x (Using Logs)

Proof - The Derivative of f(x)=a^x: d/dx[a^x]=(ln a)a^x (Using Logs)

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Proof - The Derivative of f(x)=a^x: d/dx[a^x]=(ln a)a^x (Definition)

Proof - The Derivative of f(x)=a^x: d/dx[a^x]=(ln a)a^x (Definition)

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Proof - The Derivative of f(x)=log_a(x): d/dx[log_a(x)]=1/((ln a)x)

Proof - The Derivative of f(x)=log_a(x): d/dx[log_a(x)]=1/((ln a)x)

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Proof - The Derivative of f(x)=ln(x): d/dx[ln(x)]=1/x (Implicit Diff)

Proof - The Derivative of f(x)=ln(x): d/dx[ln(x)]=1/x (Implicit Diff)

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Proof - The Derivative of f(x) = e^x: d/dx[e^x]=e^x (Implicit Differentiation)

Proof - The Derivative of f(x) = e^x: d/dx[e^x]=e^x (Implicit Differentiation)

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Proof - The Derivative of f(x) = e^x: d/dx[e^x]=e^x (Limit Definition)

Proof - The Derivative of f(x) = e^x: d/dx[e^x]=e^x (Limit Definition)

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Proof - The Chain Rule of Differentiation

Proof - The Chain Rule of Differentiation

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Proof - The Quotient Rule of Differentiation

Proof - The Quotient Rule of Differentiation

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Proof - The Product Rule of Differentiation

Proof - The Product Rule of Differentiation

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Proof - The Power Rule of Differentiation

Proof - The Power Rule of Differentiation

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Proof - The Derivative of Cosine: d/dx[cos(x)]

Proof - The Derivative of Cosine: d/dx[cos(x)]

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Proof - The Derivative of Sine: d/dx[sin(x)]

Proof - The Derivative of Sine: d/dx[sin(x)]

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Proof - the Derivative of Sum and Difference of Functions: d/dx[f(x)+g(x)]

Proof - the Derivative of Sum and Difference of Functions: d/dx[f(x)+g(x)]

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Proof - the Derivative of a Constant Times a Function: d/dx[cf(x)]

Proof - the Derivative of a Constant Times a Function: d/dx[cf(x)]

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Prove the Derivative of a Constant: d/dx[c]

Prove the Derivative of a Constant: d/dx[c]

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Prove the Limit as x Approaches 0 of (e^x-1)/x

Prove the Limit as x Approaches 0 of (e^x-1)/x

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Prove the Limit as x Approaches 0 of (1-cos(x))/x

Prove the Limit as x Approaches 0 of (1-cos(x))/x

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Prove the Limit as x Approaches 0 of sin(x)/x

Prove the Limit as x Approaches 0 of sin(x)/x

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The Squeeze Theorem

The Squeeze Theorem

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Ex 2: Use L'Hopital's Rule to Determine a Limit Approaching Zero with Trig Function

Ex 2: Use L'Hopital's Rule to Determine a Limit Approaching Zero with Trig Function

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Ex 1: Use L'Hopital's Rule to Determine a Limit Approaching Zero with Trig Function

Ex 1: Use L'Hopital's Rule to Determine a Limit Approaching Zero with Trig Function

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Ex: Use L'Hopital's Rule to Determine a Limit Approaching Zero

Ex: Use L'Hopital's Rule to Determine a Limit Approaching Zero

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Ex: Use L'Hopital's Rule to Determine a Limit Approaching Infinity

Ex: Use L'Hopital's Rule to Determine a Limit Approaching Infinity

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Ex 3: L'Hopitals Rule Involving Exponential Functions

Ex 3: L'Hopitals Rule Involving Exponential Functions

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Ex 2: L'Hopitals Rule Involving Trig Functions

Ex 2: L'Hopitals Rule Involving Trig Functions

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Ex 1: L'Hopitals Rule Involving Trig Functions

Ex 1: L'Hopitals Rule Involving Trig Functions

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Partial Proof of L'Hopital's Rule (Only Form 0/0)

Partial Proof of L'Hopital's Rule (Only Form 0/0)

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L'Hopital's Rule - Justification Using Tangent Lines (Form 0/0)

L'Hopital's Rule - Justification Using Tangent Lines (Form 0/0)

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Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 3)

Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 3)

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Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 2)

Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 2)

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Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 1)

Determine if L'Hopital's Rule Can Be Applied to a Limit (Ex 1)

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L’Hopital’s Rule: Part 2

L’Hopital’s Rule: Part 2

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L’Hopital’s Rule: Part 1

L’Hopital’s Rule: Part 1

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Ex: Newton’s Method to Approximate Zeros – 2 Iterations

Ex: Newton’s Method to Approximate Zeros – 2 Iterations

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Newton’s Method

Newton’s Method

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Ex: Related Rates - Find the Rate of Change of Revenue (Quotient Rule)

Ex: Related Rates - Find the Rate of Change of Revenue (Quotient Rule)

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Ex: Related Rates - Find the Rate of Change of Revenue

Ex: Related Rates - Find the Rate of Change of Revenue

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Ex: Related Rates Problem -- Rate of Change of Distance Between Ships

Ex: Related Rates Problem -- Rate of Change of Distance Between Ships

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Ex 2: Related Rates Problem -- Rate of Change of a Shadow from a Light Pole

Ex 2: Related Rates Problem -- Rate of Change of a Shadow from a Light Pole

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Ex: Related Rates Problem – Rate of Change of a Shadow from a Light Pole

Ex: Related Rates Problem – Rate of Change of a Shadow from a Light Pole

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Ex: Related Rates - Air Volume and Pressure

Ex: Related Rates - Air Volume and Pressure

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Ex: Related Rates - Volume of a Melting Snowball

Ex: Related Rates - Volume of a Melting Snowball

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Ex: Related Rates - Rotating Light Projecting on a Wall

Ex: Related Rates - Rotating Light Projecting on a Wall

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Ex: Related Rates - Right Circular Cone

Ex: Related Rates - Right Circular Cone

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Ex: Related Rates - Area of Triangle

Ex: Related Rates - Area of Triangle

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Ex 4: Related Rates: Ladder Problem

Ex 4: Related Rates: Ladder Problem

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Ex 3: Related Rates: Determine the Rate of Change of Volume with Respect to Time

Ex 3: Related Rates: Determine the Rate of Change of Volume with Respect to Time

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Ex 2: Related Rates: Determine the Rate of Change of the Area of a Circle With Respect to Time

Ex 2: Related Rates: Determine the Rate of Change of the Area of a Circle With Respect to Time

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Ex 1: Related Rates: Determine the Rate of Change of Profit with Respect to Time

Ex 1: Related Rates: Determine the Rate of Change of Profit with Respect to Time

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Related Rates

Related Rates

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Ex: Find dy/dx Using Implicit Differentation and the Product Rule - ax-bxy-cy^n=d

Ex: Find dy/dx Using Implicit Differentation and the Product Rule - ax-bxy-cy^n=d

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Ex: Find dy/dx Using Implicit Differentation and the Product Rule - e^(2xy)=y^n

Ex: Find dy/dx Using Implicit Differentation and the Product Rule - e^(2xy)=y^n

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Ex: Perform Implicit Differentiation and Find the Equation of a Tangent Line

Ex: Perform Implicit Differentiation and Find the Equation of a Tangent Line

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Ex: Implicit Differentiation to Determine a Second Derivative

Ex: Implicit Differentiation to Determine a Second Derivative

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Ex: Implicit Differentiation Involving a Trig Function

Ex: Implicit Differentiation Involving a Trig Function

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Ex: Implicit Differentiation - Equation of Tangent Line

Ex: Implicit Differentiation - Equation of Tangent Line

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Ex 4: Implicit Differentiation Involving a Trig Function

Ex 4: Implicit Differentiation Involving a Trig Function

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Ex 3: Implicit Differentiation Using the Product Rule and Factoring

Ex 3: Implicit Differentiation Using the Product Rule and Factoring

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Ex 2: Implicit Differentiation Using the Product Rule

Ex 2: Implicit Differentiation Using the Product Rule

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Ex 1: Implicit Differentiation

Ex 1: Implicit Differentiation

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Implicit Differentiation of Equations containing Transcendental Functions

Implicit Differentiation of Equations containing Transcendental Functions

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Implicit Differentiation

Implicit Differentiation

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Introduction to Basic Implicit Differentiation - YouTube

Introduction to Basic Implicit Differentiation - YouTube

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Ex 4: Mean Value Theorem – Quadratic Fomula Needed

Ex 4: Mean Value Theorem – Quadratic Fomula Needed

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Ex 3: Mean Value Theorem – Rational Function

Ex 3: Mean Value Theorem – Rational Function

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Ex 2: Mean Value Theorem – Cubic Function

Ex 2: Mean Value Theorem – Cubic Function

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Ex 1: Mean Value Theorem – Quadratic Function

Ex 1: Mean Value Theorem – Quadratic Function

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Proof of the Mean Value Theorem

Proof of the Mean Value Theorem

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The Mean Value Theorem

The Mean Value Theorem

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Ex 2: Rolle's Theorem with Product Rule

Ex 2: Rolle's Theorem with Product Rule

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Ex 1: Rolle's Theorem

Ex 1: Rolle's Theorem

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Proof of Rolle's Theorem

Proof of Rolle's Theorem

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Rolle’s Theorem

Rolle’s Theorem

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Ex: Use Differentials to Approximate Possible Error for the Surface Area of a Sphere

Ex: Use Differentials to Approximate Possible Error for the Surface Area of a Sphere

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Ex: Differentials - Approximate Delta y Using dy Using a Sine Function and Find Error Percent

Ex: Differentials - Approximate Delta y Using dy Using a Sine Function and Find Error Percent

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Ex: Find dy Given a Tangent Function - Requires the Chain Rule

Ex: Find dy Given a Tangent Function - Requires the Chain Rule

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Ex: Differentials: Compare delta y and dy

Ex: Differentials: Compare delta y and dy

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Ex: Using Differentials to Approximate the Value of a Cube Root.

Ex: Using Differentials to Approximate the Value of a Cube Root.

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Ex: Differentials to Approximate Propagated Error and Relative Error

Ex: Differentials to Approximate Propagated Error and Relative Error

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Ex 2: Differentials: Determine dy given x and dx

Ex 2: Differentials: Determine dy given x and dx

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Ex 1: Determine Differential y (dy)

Ex 1: Determine Differential y (dy)

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Differentials

Differentials

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Ex: Use a Tangent Line to Approximate a Cube Root Function Value – Chain Rule

Ex: Use a Tangent Line to Approximate a Cube Root Function Value – Chain Rule

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Ex: Use a Tangent Line to Approximate a Quotient

Ex: Use a Tangent Line to Approximate a Quotient

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Ex: Use a Tangent Line to Approximate a Square Root Value

Ex: Use a Tangent Line to Approximate a Square Root Value

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Tangent Line Approximation Given a Function and Derivative Function Value

Tangent Line Approximation Given a Function and Derivative Function Value

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Introduction to Differentials

Introduction to Differentials

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Ex: Determine Increasing/Decreasing Intervals and Absolute Extrema (Product Rule)

Ex: Determine Increasing/Decreasing Intervals and Absolute Extrema (Product Rule)

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Ex: Absolute Extrema of a Trigonometric Function on a Closed Interval

Ex: Absolute Extrema of a Trigonometric Function on a Closed Interval

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Ex: Absolute Extrema of a Quadratic Function on a Closed Interval

Ex: Absolute Extrema of a Quadratic Function on a Closed Interval

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Ex 2: Absolute Extrema on an Open Interval

Ex 2: Absolute Extrema on an Open Interval

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Ex 1: Absolute Extrema on an Closed Interval

Ex 1: Absolute Extrema on an Closed Interval

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Absolute Extrema of Transcendental Functions

Absolute Extrema of Transcendental Functions

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Absolute Extrema

Absolute Extrema

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The graphs of f(x), f’(x), f’’(x)

The graphs of f(x), f’(x), f’’(x)

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Ex: Given the Cost and Demand Functions, Maximize Profit

Ex: Given the Cost and Demand Functions, Maximize Profit

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Ex: Find a Demand Function and a Rebate Amount to Maximize Revenue and Profit

Ex: Find a Demand Function and a Rebate Amount to Maximize Revenue and Profit

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