Unit 2: Differentiation
Lesson 1: Review - Rules of Differentiation
Course Note: Review - Rules of Differentiation
Khan Academy Lessons:
Homework: Edwards p. 114 #11-17 (odd), 44-50 (even), p. 125 #1, 3, 9, 25, 27, 29, Chain Rule & Combinations Homework first part: #5fg, 6, second part: 3dhl, 4b, 6
Videos: The Power Rule, The Constant Multiplier Rule, The Sum & Difference Rules, The Product Rule, Differentiating Polynomials, Differentiating Integer Powers, Basic Derivative Rules, The Product Rule, The Quotient Rule, Quotient Rule Example
Khan Academy Practice: Differentiating Polynomials, Differentiating Integer Powers, Basic Derivative Rules, Product Rule, Quotient Rule
Lesson 2: Derivatives of Transcendental Functions
Course Note: Review - Rules of Differentiation for Transcendentals
Khan Academy Lessons: Differentiating Exponential Functions, Differentiating Logarithmic Functions
Homework: Larson p. 325 #41-63 (odd), p. 352 #33-51 (odd), p. 362 #37-58
Videos: Derivatives of Sine and Cosine, Derivative of e^x, Derivative of lnx, Derivatives of Tangent and Cotangent, Derivatives of Secant and Cosecant, Secant with Chain, Derivative of a^x, Derivative of a^f(x) using Chain, Derivative of logx, Derivative of log(f(x)) using Chain, Logarithmic Functions using Log Properties, Derivative of sin(ln(x^2))
Khan Academy Practice: Derivatives of Sine and Cosine, Derivatives of e^x and lnx, Derivatives of Tangent, Cotangent, Secant, and Cosecant, Differentiating Trigonometric Functions, Derivatives of Trig Functions, Derivatives of a^x and logx, Differentiate Exponential Functions, Differentiating Logarithmic Functions,
Lesson 3: Slope Curves
Course Note: Investigating Slope Curves
Homework: Investigating Slope Graphs
Videos: Derivative as Slope of a Curve
Lesson 4: Differentiability and Continuity
Course Note: Differentiability and Continuity
Khan Academy Lessons:
Homework: Differentiability and Continuity #15 on, Homework Key
Videos: Differentiability and continuity, Differentiability at a Point (Graphical), Differentiability at a Point where Differentiable (Algebraic), Differentiability at a Point where Non-Differentiable (Algebraic),
Khan Academy Practice: Differentiability at a Point (Graphical), Differentiability at a Point (Algebraic)
Lesson 5: Differentiating from Tables and Graphs
Course Note: Differentiating from Tables, Graphs, and Symbolically
Homework: Derivatives from Tables and Graphs, Homework Key
Videos: Estimating Derivatives from Tables, Derivatives using a Table, Derivatives from a Graph, Finding Derivatives from a Curve, Symbolic Differentiation, More Symbolic Differentation
Lesson 6: Implicit Differentiation
Course Note: Implicit Differentiation
Homework: Implicit Differentiation, Homework Key
Videos: Implicit Differentiation, Implicit Differentation (Worked Example), Evaluating Derivatives with Implicit Differentiation, Implicit Differentiation, Implicit Differentiation at a Point
Lesson 7: Derivatives of Inverse Functions
Course Note: Derivatives of Inverse Functions
Homework: Derivatives of Inverse Functions, Homework Key
Videos: Derivatives of Inverse Functions, Derivatives of Inverses from Equation, Derivatives of Inverses from Tables, Derivative of Arcsin, Derivative of Arccos, Derivative of Arctan
Lesson 8: Equations of Tangent Lines
Course Note: Equations of Tangent Lines
Homework: Equations of Tangent Lines #1-15, Homework Key
Videos: Finding Tangent Line Equations, Equation of a Tangent Line (Product Rule), Equations of Tangent Lines
Lesson 9: Linear Approximation
Course Note: Linear Approximation
Homework: Equations of Tangent Lines #16-27, 30, Homework Key
Videos: Local Linearization, Linear Approximation, Linear Approximation of a Rational Function