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# MATH 125 TEST 2 STUDY GUIDE MATH 125 010

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This 3 page Study Guide was uploaded by Rachel Klein on Friday February 26, 2016. The Study Guide belongs to MATH 125 010 at University of Tennessee - Knoxville taught by in Spring 2016. Since its upload, it has received 47 views. For similar materials see Basic Calculus 125 in Math at University of Tennessee - Knoxville.

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Date Created: 02/26/16

Math 125, Test 2 Study Guide Spring 2016 Chapter 7.6, Product and Quotient Rules •! The Product Rule ! " ∙ $ " = ! " $ " + (! " $′(") o! Can also be solved by multiplying out the equation and solving as a polynomial o! When there are 3+ functions ! " ∙ $ " ∙ ℎ " = ! " $ " ℎ " + (! " $ " ℎ " + ! " $ " ℎ′(") •! The Quotient Rule ! " & ! " $ " − ! " $′(") = $ " ($ " ). Chapter 7.7, Chain Rule •! The Chain Rule /0 /0 /1 /" =( /1 /" can also be written as /0 & /" ! $ " =(! $ " ∙ $′(") •! Used for composite functions o! Example of when to use chain rule: ! " =( 2" + 1 !! ! " =( " and $ " = (2" + 1 •! The General Power Rule /0 = 4(1 " ) 567 ∙ 1′(") /" o! Example of when to use chain rule: ! " = " + 2" . 9 Chapter 8.1, Higher Order Derivatives •! Original function: ! " =(3" + 4" + 2" •! First order derivative: ! " = (15" + 8" + 2 •! Second order derivative: !& " = (60" + 24" . •! Third order derivative: !&&" = (180" + 48" •! Fourth order derivative: ! 8 " = 360" + 48 9 •! Fifth order derivative: ! " = (360 A •! Sixth order derivative: ! " = 0 •! The position of any free falling object is given by B C =(−16C + D C +Eℎ !! h = height of the object when it starts to fall !! v 0 initial velocity !! t = time in seconds o! B(C) represents distance as a function of time o! B′(C) represents velocity with respect to time o! B′′(C) represents acceleration with respect to time Chapter 10.3, Derivatives of Exponential Functions •! Review of Exponential Functions F o! When the variable is in the exponent: $ " =(2 o! When the constant (in this case the constant is 2) is positive, then the function will have exponential decay to left of the y-axis and exponential growth to the right o! Properties of Exponents !! a = 1 !! a a = a x+y G H F6K !! G I=(J !! J ) = a xy !! (JL) = a bx x -x 7 !! a = GH o! Natural Number e !! Definition: As e = lim(1 + "), e = 2.71 F→Q x !! Natural exponential function is f(x) = e x x •! The Derivative of f(x) = e is f’(x) = e •! Sometimes this function can be more complicated / S F S(F) R =(R ∙ 1′(") /" Chapter 10.5, Logarithms and their Derivatives •! Quick Review of Logarithms o! Basically the opposite of an exponent o! ln" =… " e = x ln" = L(((((((( =((((((((((R = " o! No such thing as a logarithm of a negative number or a logarithm of 0 •! Basic Properties of Logarithms F o! lnR = " VWF o! R = " o! ln"0 = ln" + ln0 F o! lnK= ln" − ln0 o! ln" = 4ln" •! Derivatives of Logarithms / 1 /" ln" = " / 1 /" ln(1 " ) = 1(") ∙ 1′(")

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