Answered: 2. QUICK DERIVATIVES AND INTEGRALS a) y…

Feynman’s technique is the greatest integration method of all time

Calculus: Early Transcendentals

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

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I really need help figuring out how to do this problem, using the cheat sheet formula is needed in this equation

2. QUICK DERIVATIVES AND INTEGRALS a) y = 13x4 + 3e 4x5 s Find y'. %3D

Transcribed Image Text:2. QUICK DERIVATIVES AND INTEGRALS a) y = 13×4 + 3e 4×5 s Find y’. %3D

$*TATTOO"CHEAT SHEET - USE OFTEN! youR THE BASICS derrv. PX) MP CO) MC RX) X - fcx)+y ly CAN BE +,Ø,-) Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.}) integ %3D X *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION}) DERIVATIVES PRODUCTS AND QUOTIENTS y=x^ y'- nx^- you" u isA FUNCTION, %3D U AND V y=uv y'= u'v +uv n-1 y'=nu" (u') X IS VAR., ARE FUNCTIONS y= e" y'- u'e" e AND ny= u y'= u'v -uv' V CONSTANTS dautdin y=Lnu y's 4 LOGS AND EXPONENTS y=a" y'=a"u’ına ) WHERE u IS A FUNC, INTEGRALS yoa" g =a*x' ina fais const, + X +K , n#-1 X IS VARVABLE Fa*(1) Lna ntl +k, n+-1 in(e*) =x (SIMPLIFIED, NOT DERIVATIVE ) =X (SIMPUFIED, NOT DERIVATIVE) + e" +K In(MN)= Ln M+ unN in (A) - LnM -UnN Lin(MP) = y=lagax a =x 4- Ju'u"dx → inu tK n- STEPS WHERE M EN ARE FUNCTIONS. (CONVERSIONS NOT DERIVATIVES) Pn M WHICH INTEGRAL? 1) MAKE IT 2) FIND U; CREATE U' 3) WE HAVE 4) MAKE IT LOOK LIKE TEMPLATE 5) PERFORM INTEGRAL PRETTY: WE WANT. CHANGE OF BASE: y=loga x -LogX = In x loga DEFINITE INTEGRALS ALSO Una y=Sax'dx = afx*ax y=S(ax^+bx") dx Fa) = ffondx JHondk = FO = F(b) - F(a) "dx %3D %3D$

Transcribed Image Text:*TATTOO”CHEAT SHEET – USE OFTEN! youR THE BASICS derrv. PX) MP CO) MC RX) X – fcx)+y ly CAN BE +,Ø,-) Xf’cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.}) integ %3D X *f”Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION}) DERIVATIVES PRODUCTS AND QUOTIENTS y=x^ y’- nx^- you” u isA FUNCTION, %3D U AND V y=uv y’= u’v +uv n-1 y’=nu” (u’) X IS VAR., ARE FUNCTIONS y= e” y’- u’e” e AND ny= u y’= u’v -uv’ V CONSTANTS dautdin y=Lnu y’s 4 LOGS AND EXPONENTS y=a” y’=a”u’ına ) WHERE u IS A FUNC, INTEGRALS yoa” g =a*x’ ina fais const, + X +K , n#-1 X IS VARVABLE Fa*(1) Lna ntl +k, n+-1 in(e*) =x (SIMPLIFIED, NOT DERIVATIVE ) =X (SIMPUFIED, NOT DERIVATIVE) + e” +K In(MN)= Ln M+ unN in (A) – LnM -UnN Lin(MP) = y=lagax a =x 4- Ju’u”dx → inu tK n- STEPS WHERE M EN ARE FUNCTIONS. (CONVERSIONS NOT DERIVATIVES) Pn M WHICH INTEGRAL? 1) MAKE IT 2) FIND U; CREATE U’ 3) WE HAVE 4) MAKE IT LOOK LIKE TEMPLATE 5) PERFORM INTEGRAL PRETTY: WE WANT. CHANGE OF BASE: y=loga x -LogX = In x loga DEFINITE INTEGRALS ALSO Una y=Sax’dx = afx*ax y=S(ax^+bx”) dx Fa) = ffondx JHondk = FO = F(b) – F(a) “dx %3D %3D

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