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Calculus I (MAT 145) Dr. Day Mon day February 18, 2019. Derivative Shortcuts ( Ch 3) Sums, Differences, Product, Quotients Constants, Powers, Exponential Functions Trig Functions The Chain Rule! Return Quiz # 5. Warm up!. Calculate each derivative. Use correct notation!.
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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 MAT 145
Warm up! Calculate each derivative. Use correct notation! • . MAT 145
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Practice Derivative Rules 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. MAT 145
Using Derivative Patterns Supposes(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. MAT 145
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? MAT 145
Practice Derivative Rules MAT 145
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. Use the chain rule when e'eryou find The derivative of a function compositionally defined. MAT 145
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