Calculus I (MAT 145) Dr. Day Monday February 18, 2019 Derivative Shortcuts (Ch 3) Sums, Differences, Product, Quotients Constants, Powers, Exponential Functions Trig Functions The Chain Rule! Return Quiz #5 Monday, February 18, 2019 MAT 145

Warm up! . Calculate each derivative. Use correct notation! Monday, February 18, 2019 MAT 145

Sums, differences, exponentials, & products of constants and functions Monday, February 18, 2019 MAT 145

Derivatives of Trig Functions Monday, February 18, 2019 MAT 145

Monday, February 18, 2019 MAT 145

Monday, February 18, 2019 MAT 145

Practice Derivative Rules Monday, February 18, 2019 MAT 145

Using Derivative Patterns For f(x) = 2x2 – 3x + 1: Calculate f’(x). Determine an equation for the line tangent to the graph of f when x = −1. Determine all values of x that lead to a horizontal tangent line. Determine all ordered pairs of f for which f’(x) = 1. Monday, February 18, 2019 MAT 145

Using Derivative Patterns MAT 145 Suppose s(x), shown below, represents an object’s position as it moves back and forth on a number line, with s measured in centimeters and x in seconds, for x > 0. Calculate the object’s velocity and acceleration functions. Is the object moving left or right at time x = 1? Justify. Determine the object’s velocity and acceleration at time x = 2. Based on those results, describe everything you can about the object’s movement at that instant. Write an equation for the tangent line to the graph of s at time x = 1. Monday, February 18, 2019

Using Derivative Patterns Determine the equation for the line tangent to the graph of g at x = 4. Determine the equation for the line normal to the graph of g at x = 1. At what points on the graph of g, if any, will a tangent line to the curve be parallel to the line 3x – y = –5? Monday, February 18, 2019 MAT 145

Practice Derivative Rules - Answers Monday, February 18, 2019 MAT 145

Practice Derivative Rules Monday, February 18, 2019 MAT 145

Practice Derivative Rules - Answers Monday, February 18, 2019 MAT 145

Derivatives of Composite Functions Monday, February 18, 2019 MAT 145

Derivatives of Composite Functions (3.4) Monday, February 18, 2019 MAT 145

Here's a function in a function And your job here is to find THE CHAIN RULE WORDS BY: JOHN A. CARTER TUNE: "CLEMENTINE" Here's a function in a function And your job here is to find The derivative of the whole thing With respect to x inside. Call the outside f of u And call the inside u of x. Differentiate to find df/du And multiply by du/dx. Use the chain rule. Use the chain rule when e'er you find The derivative of a function compositionally defined. Monday, February 18, 2019 MAT 145

Derivatives of Composite Functions (3.4) Monday, February 18, 2019 MAT 145

Derivatives of Composite Functions Monday, February 18, 2019 MAT 145

Composite Functions Monday, February 18, 2019 MAT 145