Chapter 2 Sections 5.3 and 5.4
Chapter 2 Sections 5.3 and 5.4 MTH 162
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This 3 page Class Notes was uploaded by Jack Magann on Friday February 6, 2015. The Class Notes belongs to MTH 162 at University of Miami taught by Dr. Bibby in Spring2015. Since its upload, it has received 109 views. For similar materials see Calculus 2 in Mathematics (M) at University of Miami.
Reviews for Chapter 2 Sections 5.3 and 5.4
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Date Created: 02/06/15
Calculus 2 Chapter 53 quot Natural Exponential Function ex i cxp 1 exylnyx Therefore 1 1n ex x For the derivative for ex we use logarithmic differentiation yex lnylnex gt lnyx Take the derivative ofboth sides gt iy 1 gt y y gt y 2 ex d gt quotquot Therefore ex 2 ex This is a little different when the chain rule is applied at du e e dx dx For the integral f ex 2 ex C EX 1 x 1 x 1 x x 1yEe Slnx Ee cosxge Slnx e cosx 1 1 y 5ex cosx ex s1nx ex Slnx ex cosx 5Zex51nx exsmx 2 xey yex xeyy ey yex y ex gt xexy exy yex ey gt I x x x y Izyexey 31068 e ye e gt y xeLex 1 x2xex 2x2xex 3gtyx2exx lnyx1 x2ex gt EV39ZW gt y ym I 2 x x 2x2xex y x e x2ex 4 fexxex 1dx u substitution u 2 996 1 du exdx 3 fexVex1dx fxZdu u C ex15C Calculus 2 Chapter 54 Derivative of regular log functions If you recall the change of base formula loga N 2 11111 1 Then 10 x lnx i 1nx 1 dx ga dx lna lna dx xlna Derivative and integral of number to the power of X 1 101quot Use logarithmic differentiation to solve this dx 1nylnax gt 1nyxlna gt 3 11y 21na This is true since In a is a constant y aquot In a or with the chain rule 1a aud ulna dx dx 2 faxlnadxaxC faxiaxC lna Ex 1 y 10g2 1 1 1 x 5 1 1 x 1 1 1 1 n ln ln ln 2 y ln2 x2 21n2 x2 ln 22 x x ln4 x x2 2 gx 5603 g x 5603 ln5 sinx 3fx22xdxfx2dxf2xdx x32xC 4f33dxf1dxf131 xdx u1 x du 1dx x f3udu2x i31 xC ln3 All these notes are from a Calculus 2 class run by Dr Patrick Dibby at the University of Miami A majority of the problems used by the teacher and copied in these notes are taken from the textbook Essential Calculus Second edition By James Stewart Citation Stewart James Essential Calculus 2nd ed Np Cangage Learning 2013 Print
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