Calculus I - Derivatives of Polynomials & Exponentials PDF

Section 3.1: Derivatives of Polynomials & Exponentials I. The Constant & Power Rules for Derivatives Derivative of a Constant c Cx c Proof...

Section 3.1: Derivatives of Polynomials & Exponentials I. The Constant & Power Rules for Derivatives Derivative of a Constant c Cx c Proof QED Derivative of the Identity Proof QED The Power Rule n Proof I 1 I if  The General Power Rule: Example 1 A. 4 5 1 5 fickle 5 112 B. 5 3 X gum Ext l EI 3.1415913 C. constant K h'Cx O II. The Constant Multiple & Sum Rules for Derivatives The Constant Multiple Rule c f or Proof QED Example 2 A. 54 f f 35 4 f 43 15  B. t t t't'te t z gie Z t Lt Zzz Z RE g C. 45 3 45 13 Iz t 5 L e a hilts Ez g 13 le lad 1 h 16 h IE 9ft The Sum Rule f g Proof QED Example 3 A. B. C. Example 4 3 X A. X5 4 5 f'Get 5 sq 4 3 f 47 5 3 44 3 f Cx 5.4 3.3 3 2 a e 20 9 y B. w i E 1 N I I Tz Ex e Iz X t 0 52 I 112 2 12 rat I ZX zrx  C. list It let 9 2 f It It 3 E z I D 16 I 19.22T f It 6 118 t f It D. Ap PPI z Ap p gp l l I A 1p g Ip Z I Ap q Lp Apa I Example 5 A.. 2 f x 3 6X o B. whee fickle slope of tangent lineatx horizontal tangent when f2 O Cx 1 Lex O 3 0 3 1 21 h or X 2 0 I 0 3 or X Z X O  C. 43 3 2 f Lk 3 4 13 13CD2 1 e f i on ftx7 the point Cl 41 point Xi Yi ontangentline f l d slopeof tangent 2 telex f x 23 3412 6 i 9 f Cc Slope Equation of tangentXi m mLx y y y 4 9 K I 7 9 9 4 y 9 5 y Example 6 t A. B.  C. Example 7 III. The Derivative of 2X 3 TX  Ty Ews b X e y ye Ine eh X Logee e Y ex the rate of change for an exponential function is proportional to the exponential function itself. e k r store e Definition of the number e e I  Derivative of the Natural Exponential Function y Example 8 A. flexi exto e FEEL y4 IEg c f y C f B. e e5 e5 ex y f Liye e5 ex f G sexts C. Tie4 I 4 f Cx 4e f'Cx 4 ex  n powerRule y x a n I a y n X y yl ax Lora 6 y X X 5 Z y 6 y y n27 zX 4 514 y 4 y E y p'T IT I zT y