~~META:title=Chapter 2~~ ~~NOTOC~~ \\ ===== The Derivative as a Function =====\\ //Section 2.2 in Stewart's Calculus.// [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.2_derivative_function.pdf|Classroom Slides PDF]] \\ ===== Differentiation Formulas ===== {{youtube>qFHSXnXSaS4}} //Section 2.3 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Derivative formulas for powers and roots.\\ * Derivative formulas for sums/differences/products/quotients. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.3_differentiation_formulas.pdf|Classroom Slides PDF]] \\ ===== Trigonometric Derivatives ===== {{youtube>tafh4ANt-gs}} //Section 2.4 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Familiarity with the limit of sin(x)/x as x approaches zero. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.4_trig_derivatives.pdf|Classroom Slides PDF]] \\ ===== The Chain Rule ===== {{youtube>bNwaBeNamr0}} //Section 2.5 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Composition and rates of change.\\ * Chain Rule Formula. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.5_chain_rule.pdf|Classroom Slides PDF]] \\ ===== Implicit Differentiation ===== {{youtube>LUtciqbWhyw}} {{youtube>hUEDDP7CvPs}} \\ //Section 2.6 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * An equation implicitly defines many functions.\\ * Implicitly versus explicitly defined functions.\\ * Basics of Implicit Differentiation. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.6_implicit_differentiation.pdf|Classroom Slides PDF]] \\ ===== Rates of Change in the Sciences ===== {{youtube>ZImKZBJlkRE}} //Section 2.7 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__ \\ * Instantaneous Rates of Change are everywhere! [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.7_sciences.pdf|Classroom Slides PDF]] \\ ===== Related Rates ===== {{youtube>W6sPil54GQ8}} {{youtube>Q0wgb9pYMoo}} \\ //Section 2.8 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * Rates of change can be found by implicitly differentiating an equation. This technique is useful in obtaining information in natural, less mathematical, settings.\\ [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.8_related_rates.pdf|Classroom Slides PDF]] \\ ===== Linearization and Differentials ===== {{youtube>1rtvN3dcxbU}} {{youtube>2bf00We0FNg}} \\ //Section 2.9 in Stewart's Calculus.//\\ \\ __**Preclass Learning Objectives:**__\\ * Lines are functions, even tangent lines.\\ * Linearization of a function f(x) approximates the values of f(x).\\ * The change along the y-axis can be approximated with linearization. [[http://www2.math.binghamton.edu/lib/exe/fetch.php/calculus/resources/calculus_flipped_resources/2.9_linearization_differentials.pdf|Classroom Slides PDF]] \\