Definition Of Derivative
1 hr 16 min 6 Examples
- Developing the formula and notation of the definition of derivative
- Calculate the derivative a line using the limit definition (Example #1)
- Graph and find the derivative x-squared using the limit definition (Example #2)
- Find and evaluate the derivative of a parabola using the definition (Example #3)
- Use the limit definition of derivative to calculate and evaluate a square root function (Example #4)
- Determine the derivative of the rational function and evaluate at given points (Example #5)
- Find the derivative of an absolute value function using the limit definition (Example #6)
Power Rule
1 hr 16 min 17 Examples
- What is the power rule? Constant Multiple Rule? Constant Rule? Sum and Difference Rule?
- Use the power rule to find the derivative of each function (Examples #1-5)
- Transform the use the power rule to find the derivative (Examples #6-8)
- Simplify then apply the power rule to calculate derivative (Examples #9-10)
- Find the derivative at the indicated point (Example #11)
- Evaluate the derivative at the indicated point (Examples #12-13)
- Understanding Derivative Properties: True or False (Examples #14-17)
Product Rule
1 hr 15 min 8 Examples
- Overview of the Product Rule for differentiation
- Find the derivative using the product rule (Examples #1-2)
- Find the derivative and simplify fully (Example #3)
- Evaluate the derivative to the given value (Examples #4-5)
- Transform then differentiate using product rule to find f'(c) (Example #6)
- Given the graph of f and g, find the derivative of fg at c (Example #7a-c)
- Differentiate the algebraic function of the product of three terms at indicated point (Example #8)
Quotient Rule
1 hr 6 min 7 Examples
- Overview of the Quotient Rule
- Find the derivative and simplify (Example #1)
- Differentiate using the quotient rule (Example #2)
- Evaluate the derivative at the indicated pont (Example #3)
- Find f'(c) using the quotient rule (Example #4)
- Transform then differentiate the algebraic fraction (Example #5)
- Factor and then find the derivative (Example #6a)
- Use the product rule and quotient rule (Example #6b)
- Use the graphs of f and g to evaluate the derivative of the algebraic fraction (Example #7)
Chain Rule
1 hr 6 min 7 Examples
- Quick review of the Power, Product and Quotient Rules
- What is the Chain Rule?
- Use the chain rule to find the derivative of composite functions (Examples #1-3)
- Find the instantaneous rate of change using the product rule and chain rule (Example #4)
- Use the chain rule and quotient rule to find the derivative (Example #5)
- Determine the instantaneous rate of change using the quotient rule and chain rule (Example #6)
- Utilize a graph to evaluate the derivative of a composite function (Example #7a-b)
Derivative Rules
1 hr 24 min 13 Examples
- Quick review of the derivative rules so far
- Find the derivative of the algebraic function using the power rule (Examples #1-3)
- Find the derivative using the product rule (Example #4)
- Find the derivative using the chain rule (Example #5)
- Calculate the derivative using the product rule and the chain rule (Example #6)
- Find F'(a) given F(x)=f(g(x)) (Example #7)
- Evaluate the derivative at the indicated point using the chain rule (Example #8)
- Find the derivative using the chain rule and quotient rule (Example #9)
- Differentiate using the quotient rule (Example #10)
- Differentiate using the chain rule and quotient rule (Example #11)
- Calculate the derivative using the product and chain rule and simplify using the GCF (Example #12)
- Calculate the derivative using the quotient rule and chain rule and simplify (Example #13)
Derivative Of Exponential Function
58 min 11 Examples
- Review of Exponential Properties
- Derivative Formula for Exponential Functions
- Find the derivative of the exponential function (Examples #1-2)
- Calculate the derivative of the exponential function (Examples #3-5)
- Use the product, chain or quotient rules with exponential derivative rule (Examples #6-8)
- Differentiate the exponential function (Example #9)
- Evaluate the derivative at the indicated point (Examples #10-11)
Derivatives Of Logarithmic Functions
1 hr 12 min 11 Examples
- Logarithmic properties and formula for derivative of logarithms
- Find the derivative of the log function (Examples #1-2)
- Differentiate the logarithmic function (Examples #3-5)
- Simplify using properties of logarithms then differentiate (Example #6)
- Use the product rule to find the derivative of the log function (Example #7)
- Differentiate using the quotient rule then differentiate using log properties (Example #8)
- Find f'(c) by using the quotient rule and log derivatives (Example #9)
- Evaluate the derivative at the indicated point (Examples #10-11)
Trig Derivatives
1 hr 33 min 17 Examples
- Trigonometric Derivative Formulas and rules
- Find the derivative of the trigonometric function (Examples #1-6)
- Find the trig derivative (Examples #7-9)
- Calculate the derivative of the trig function (Examples #10-13)
- Use the rules of derivatives to calculate the rate of change (Examples #14-15)
- Evaluate the derivative at the indicated point (Examples #16-17)
Inverse Trig Derivatives
1 hr 5 min 16 Examples
- Graphs and properties of inverse trigonometric functions
- Evaluate each inverse trig function (Example)
- Six Inverse Trigonometric Derivative Formulas and Proof
- Find the derivative of the inverse trig function (Examples #1-6)
- Calculate the derivative of the inverse trig function (Examples #7-10)
- Find the inverse trig derivative (Examples #11-12)
- Calculate the inverse trig derivative (Examples #13-14)
- Find the slope of the tangent line at the indicated value (Examples #15-16)
Hyperbolic Trig Functions
55 min 15 Examples
- Properties and Derivative Formulas for Hyperbolic Trig Functions
- Examples #1-3: Find the Derivative of the Hyperbolic Function
- Examples #4-6: Find the Derivative of the Hyperbolic Function
- Examples #7-8: Find the Derivative of the Hyperbolic Function
- Examples #9-10: Find the Derivative of the Hyperbolic Function
- Derivative Formulas for Inverse Hyperbolic Trig Functions with Example #11
- Example #12: Find the Derivative of the Inverse Hyperbolic Function
- Example #13: Find the Derivative of the Inverse Hyperbolic Function
- Example #14: Find the Derivative of the Inverse Hyperbolic Function
- Example #15: Find the Derivative of the Inverse Hyperbolic Function
Derivative of Inverse Functions
1 hr 1 min 11 Examples
- Properties of Inverses and How to find Inverses (Example #1-3)
- Using the graph evaluate the function and its inverse at various points (Example #4a-j)
- Properties and Derivative of Inverse Formula (Example #5)
- Find the derivative of the inverse at a (Examples #6-9)
- Use synthetic division to help find the derivative of the inverse (Examples #10-11)
Implicit Differentiation
1 hr 36 min 15 Examples
- How do you take a derivative implicitly? (Examples #1-3)
- Find the derivative implicitly (Examples #4-7)
- Use implicit differentiation to find the derivative (Examples #8-9)
- Find dy/dx and evaluate at the indicated point (Example #10-11)
- Use implicit differentiation and evaluate at the indicated point (Examples #12-13)
- Find the slope of the tangent line to the curve implicitly (Examples #14-15)
Higher Order Derivatives
1 hr 38 min 12 Examples
- Overview of Higher Order Differentiation
- Twelve Examples
Logarithmic Differentiation
43 min 7 Examples
- Overview of Logarithmic Properties and Logarithmic Differentiation
- Example #1: Use Logarithmic Differentiation to avoid the Product Rule
- Example #2: Use Logarithmic Differentiation to avoid the Quotient Rule
- Examples #3-4: Use Logarithmic Differentiation
- Example #5: Use Logarithmic Differentiation
- Examples #6-7: Use Logarithmic Differentiation
Average Rate Of Change Calculus
1 hr 6 min 11 Examples
- Average Rate of Change Formula (Example #1)
- Given a table calculate the average rate of change over specified interval (Example #2a-c)
- Calculate the average rate of change for the function on the closed interval (Examples #3-5)
- Average Rate of Change vs Instantaneous Rate of Change
- Calculate the instantaneous rate of change at a point (Examples #6-7)
- Find the instantaneous and average rate of change for wind chill (Example #8a-b)
- Overview of Instantaneous and Average Velocity and Acceleration
- Given the position function find displacement instantaneous and average velocity and acceleration (Example #9a-e)
- Given the position function find the instantaneous and average velocity and acceleration (Example #10a-d)
- What is the value of c for which the instantaneous is the same as the average rate of change (Example #11)
L’Hopitals Rule
1 hr 46 min 17 Examples
- Overview of L’Hospital’s Rule for limits of indeterminate form?
- Evaluate the indeterminate limit (Examples #1-3)
- Find the limit using l’hopital’s rule (Examples #4-9)
- Transform then find the limit using l’hospital’s rule (Examples #10-13)
- Use L’Hopital’s rule more than once to find the limit (Examples #14-15)
- Use logarithmic differentiation and l’Hopital’s rule to evaluate the limit (Examples #16-17)
Equation Of Tangent Line
1 hr 2 min 10 Examples
- Summary of Equations of Lines and when lines are Parallel and Perpendicular
- Write the equation of the tangent line to the curve at the point (Examples #1-2)
- Write the equation of the line tangent to the curve (Examples #3-6)
- Write the equations of the tangent and normal lines to the curve (Examples #7-8)
- Find the equation of the tangent line and normal line (Example #9)
- Find all points where the tangent line is parallel to the axis (Example #10)
Linear Approximation
1 hr 17 min 13 Examples
- What is Linear Approximation and Linearization?
- Find the linear approximation (Example #1)
- Find the tangent line approximation (Examples #2-3)
- Use linear approximation to estimate the given number (Examples #4-6)
- What are differentials?
- Find the differential of the function (Examples #7-9)
- Evaluate the differential dy (Examples #10-11)
- Use differentials to approximate the given number (Example #12)
- Use differentials to approximate cos31.5 (Example #13)
Continuity And Differentiability
1 hr 4 min 10 Examples
- What is continuity and differentiability?
- Using the graph of f(x) state the numbers at which f is not continuous nor differentiable (Example #1)
- How do you prove differentiability?
- Prove whether the absolute value graph is differentiable (Examples #2-3)
- Determine whether the piecewise function is differentiable (Examples #4-5)
- Find the values of a, b, and c given f is a differentiable function (Examples #6-7)
- Find the values of b and c given f(x) is a differentiable function (Example #8)
- True or False: dis f(x) continuous? differentiable? (Example #9a-c)
- Consider the graph and determine the intervals of continuity and differentiability (Example #10)
Derivatives Using Charts
59 min 8 Examples
- Given the table of selected values of two differentiable functions, find p'(2) given p(x)=xf(x) (Example #1a)
- Find q'(-2) given q(x)=3f(x)g(x) (Example #1b)
- Find r'(0) given r(x)=f(x)/g(x) (Example #1c)
- Find s'(1) given s(x)=f(g(x)) (Example #1d)
- If T(x)=(2-f(x))/g(x) and T'(2)=4 find g'(2) (Example #1e)
- Let f ang g be differentiable functions with select values of x displayed in the chart, use the chain rule to find the following (Example #2a-b))
- Let f ang g be differentiable functions with select values of x displayed in the chart, write the equation fo the tangent line (Example #2c)
- Using the graph of f and g, find the following derivative at the specified point (Example #3a-c)
Limit Definition Of Derivative
44 min 11 Examples
- How to recognize the definition of derivative?
- Evaluate the limit (Example #1)
- Use derivative rules to evaluate the limit (Examples #2-4)
- Evaluate the limit using derivative rules (Examples #5-6)
- Find the derivative at a point given a limit (Examples #7-8)
- Use derivatives to find the value of the limit (Examples #9-11)
Newton’s Method
34 min 3 Examples
- Overview of Newton’s Method
- Three Examples using Newton’s Method to approximate a solution
Related Rates
2 hr 9 min 9 Examples
- Tips and Strategies for solving Related Rates problems
- Find the change in area when a pebble is dropped into a pond (Example #1)
- Change of area when air is being pumped into spherical balloon (Example #2)
- What is the change in volume as edges of cube expand (Example #3)
- Find the speed of airplane flying over radar station (Example #4)
- At what rate is the height of the cone changing (Example #5)
- Find the rate of the depth of water for a conical tank (Example #6)
- Find the speed of the boat being pulled by a winch (Example #7)
- Calculate how fast the tip of a shadow moving away from street light (Example #8)
- How fast is the top of the ladder moving down the wall (Example #9a)
- How fast is the area of the triangle changing (Example #9b)
- Find the rate of the angle between the top of the ladder and the wall (Example #9c)
Chapter Test
3 hr 6 min 45 Examples
- 45 Challenging Practice Problems
- Combining All Derivative Rules
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment