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ds 2. Find dx if y = In [(2x3 + 7)(9x – 2x²)]s Hint: Use the Tattoo and the Properties of Logs

ds 2. Find dx if y = In [(2x3 + 7)(9x – 2x²)]s Hint: Use the Tattoo and the Properties of Logs

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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This is the question and I need help and want to know steps, plus which of the tattoo formulas i have to use if needed
dS 2. Find if y = In [(2x3 + 7)(9x – 2x²)]³ dx Hint: Use the Tattoo and the Properties of Logs
Transcribed Image Text:dS 2. Find if y = In [(2x3 + 7)(9x – 2x²)]³ dx Hint: Use the Tattoo and the Properties of Logs
*TATTOO"CHEAT SHEET - USE OFTEN! youR THE BASICS derv. PX) MP CO) MC RX) MR X→ fcx)+y (ly CAN BE +,Ø,-) X f'x) SLOPE(SLOPE CAN BE +,Ø, integ. - {0 = MAx OR MIN OR H.P.I.3) X *f"(x) + CONCAVITY (CONCAVITY IS ,A,Ø { Bis POINT OF INFLECTION}) DERIVATIVES PRODUCTS AND QUOTIENTS u isA FUNCTION, X IS VAR., e AND n y= u y'= u'v -uv' y=x^ y'= nxn-i U AND V youv y'- u'v+uv' %3D n-I y'= nu" (u') y=e" y'- u'e" y=Lnu y'= 4 doutdin y=u^ ARE FUNCTIONS CONSTANTS LOGS AND EXPONENTS y=a" y'=a"u'ına ) WHERE U y-a* y = a*x' In a fa is const, Fa*(1) ina INTEGRALS IS A FUNC, x^dx +K, n+-I X IS VARVABLE ntl dx → U' +k, n+-1 Un(e*) =x (SIMPLIFIED, NOT DERIVATI VE ) =X (SIMPUFIED, NOT DERIVATIVE) y= Ju'e"dr → e" + k in(MN) = Ln M+ inN in (A) - LnM -UnN in (M) = PlnM y= logax ay =x WHERE M » In u +K n=-l EN ARE STEPS FUNCTIONS. (CONVERSIONS NOT DERIVATIVĖS 1) MAKE IT PRETTY. WHICH INTEGRAL? 2) FIND U; CREATE U' 3) WE HAVE 4) MAKE IT LOOK LIKE TEMPLATE 5) PERFORM INTEGRAL WE WANT. CHANGE OF BASE: y=loga x loga DEFINITE INTEGRALS log X In X %3D ALSO Una y=Jax^dx = afx°dx Scan" y= J(ax^+bx") dx SFondh Fo = Fb) - Fla) Jfandk=Fx) %3D %3D a
Transcribed Image Text:*TATTOO"CHEAT SHEET - USE OFTEN! youR THE BASICS derv. PX) MP CO) MC RX) MR X→ fcx)+y (ly CAN BE +,Ø,-) X f'x) SLOPE(SLOPE CAN BE +,Ø, integ. - {0 = MAx OR MIN OR H.P.I.3) X *f"(x) + CONCAVITY (CONCAVITY IS ,A,Ø { Bis POINT OF INFLECTION}) DERIVATIVES PRODUCTS AND QUOTIENTS u isA FUNCTION, X IS VAR., e AND n y= u y'= u'v -uv' y=x^ y'= nxn-i U AND V youv y'- u'v+uv' %3D n-I y'= nu" (u') y=e" y'- u'e" y=Lnu y'= 4 doutdin y=u^ ARE FUNCTIONS CONSTANTS LOGS AND EXPONENTS y=a" y'=a"u'ına ) WHERE U y-a* y = a*x' In a fa is const, Fa*(1) ina INTEGRALS IS A FUNC, x^dx +K, n+-I X IS VARVABLE ntl dx → U' +k, n+-1 Un(e*) =x (SIMPLIFIED, NOT DERIVATI VE ) =X (SIMPUFIED, NOT DERIVATIVE) y= Ju'e"dr → e" + k in(MN) = Ln M+ inN in (A) - LnM -UnN in (M) = PlnM y= logax ay =x WHERE M » In u +K n=-l EN ARE STEPS FUNCTIONS. (CONVERSIONS NOT DERIVATIVĖS 1) MAKE IT PRETTY. WHICH INTEGRAL? 2) FIND U; CREATE U' 3) WE HAVE 4) MAKE IT LOOK LIKE TEMPLATE 5) PERFORM INTEGRAL WE WANT. CHANGE OF BASE: y=loga x loga DEFINITE INTEGRALS log X In X %3D ALSO Una y=Jax^dx = afx°dx Scan" y= J(ax^+bx") dx SFondh Fo = Fb) - Fla) Jfandk=Fx) %3D %3D a
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Given,          y=ln2x3+79x-2x25

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