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"Calculus and its applications: 1.5" - Objective: differentiate using the power rule or the sum-difference rule, differentiate a constant or a constant times a function, determine points at which a tangent line has a specified slope. | 2012 Pearson Education, Inc. All rights reserved Slide 1.51- Differentiation Techniques: The Power and Sum-Difference Rules OBJECTIVE Differentiate using the Power Rule or the Sum-Difference Rule. Differentiate a constant or a constant times a function. Determine points at which a tangent line has a specified slope. 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Leibniz’s Notation: When y is a function of x, we will also designate the derivative, , as which is read “the derivative of y with respect to x.” 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- THEOREM 1: The Power Rule For any real number k, 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Example 1: Differentiate each of the following: a) b) c) a) 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules b) c) 2012 Pearson Education, Inc. All rights reserved Slide 1.5- 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules Quick Check 1 a.) Differentiate: (i) ; (ii) b.) Explain why , not . 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Example 2: Differentiate: a) b) 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- THEOREM 2: The derivative of a constant function is 0. That is, 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- THEOREM 3: The derivative of a constant times a function is the constant times the derivative of the function. That is, 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Example 3: Find each of the following derivatives: a) b) c) a) 1.5 Differentiation Techniques: The Power Rule and . | 2012 Pearson Education, Inc. All rights reserved Slide 1.51- Differentiation Techniques: The Power and Sum-Difference Rules OBJECTIVE Differentiate using the Power Rule or the Sum-Difference Rule. Differentiate a constant or a constant times a function. Determine points at which a tangent line has a specified slope. 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Leibniz’s Notation: When y is a function of x, we will also designate the derivative, , as which is read “the derivative of y with respect to x.” 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- THEOREM 1: The Power Rule For any real number k, 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide 1.5- Example 1: Differentiate each of the following: a) b) c) a) 1.5 Differentiation Techniques: The Power Rule and Sum-Difference Rules b) c) 2012 .
