"Calculus and its applications: " - 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 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 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.” Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide THEOREM 1: The Power Rule For any real number k, Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide Example 1: Differentiate each of the following: a) b) c) a) Differentiation Techniques: The Power Rule and Sum-Difference Rules b) c) 2012 Pearson Education, Inc. All rights reserved Slide 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 Example 2: Differentiate: a) b) Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide THEOREM 2: The derivative of a constant function is 0. That is, Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide THEOREM 3: The derivative of a constant times a function is the constant times the derivative of the function. That is, Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide Example 3: Find each of the following derivatives: a) b) c) a) Differentiation Techniques: The Power Rule and . | 2012 Pearson Education, Inc. All rights reserved Slide 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 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.” Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide THEOREM 1: The Power Rule For any real number k, Differentiation Techniques: The Power Rule and Sum-Difference Rules 2012 Pearson Education, Inc. All rights reserved Slide Example 1: Differentiate each of the following: a) b) c) a) Differentiation Techniques: The Power Rule and Sum-Difference Rules b) c) 2012 .
