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Class Note for MATH 1314 with Professor Gross at UH 2

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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 38 views.

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Date Created: 02/06/15
M1314 Lesson 4 1 Math 1314 Lesson 4 Basic Rules of Differentiation We can use the limit de nition of the derivative to nd the derivative of every function but it isn t always convenient Fortunately there are some rules for nding derivatives which will make this easier First a bit of notation 1 fx is a notation that means the derivative of f with respect to x evaluated at x Rule 1 The Derivative of a Constant c 0 where c is a constant Example 1 If fx l7 nd f39x Rule 2 The Power Rule xquot me for any real number 71 Example 2 If fx x5 nd f39x Example 3 If fx 6 nd f39x M1314 Lesson 4 Example 4 If fx i3 nd IMO x Rule 3 Derivative of a Constant Multiple of a Function cfx cdi fx where c is any real number x Example 5 If fx 3xquot nd f39x Example 6 If fx 5 nd f39x Rule 4 The SumDifference Rule immigmlfxigx Example 7 Find the derivative fx 4x3 2x2 4 x M 13 14 Lesson 4 Rule 5 The Derivative of the Exponential Function 61 x x 7 e e Example 8 Find the derivative fx J 4x3 2 66 Rule 6 The Derivative of an Exponential Function base is not 2 d 7 a In a r a I i l Example 9 Find the derivative f x 4x Rule 7 The Derivative of the Logarithmic Function d 1 iln x 7 rovidedx 0 dx w p a x Example 10 Find the derivative fx 5x 2 6 1nx M1314 Lesson 4 From this lesson you should be able to State the basic rules for nding derivatives Select the appropriate rule to use for a given problem Find the derivative of a function using the basic rules

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