I really need help figuring out how to do this problem, using the cheat sheet formula provided c) Find the derivative of y = In{(7x3 + 4) V3x + 10} *TATTOO"CHEAT SHEET - USE OFTEN!youRTHE BASICSderrv.PX) MPCO) MCRX)X - fcx)+y ly CAN BE +,Ø,-)Xf'cx)+SLOPE(SLOPE CAN BE +,Ø,- §Ø = MAX OR MIN OR H. P.I.})integ%3DX *f"Cx) + CONCAVITY (CONCAVITY IS U,A,Ø {0iS POINT OF INFLECTION})DERIVATIVESPRODUCTS AND QUOTIENTSy=x^ y'- nx^-you"u isAFUNCTION,%3DU AND Vy=uv y'= u'v +uvn-1y'=nu" (u') X IS VAR.,AREFUNCTIONSy= e"y'- u'e"e AND ny= u y'= u'v -uv'VCONSTANTSdautdiny=Lnu y's 4LOGS AND EXPONENTSy=a" y'=a"u’ına ) WHERE uIS A FUNC,INTEGRALSyoa" g =a*x' ina fais const,+ X +K , n#-1X IS VARVABLEFa*(1) Lnantl+k, n+-1in(e*) =x (SIMPLIFIED, NOT DERIVATIVE )=X (SIMPUFIED, NOT DERIVATIVE)+ e" +KIn(MN)= Ln M+ unNin (A) - LnM -UnNLin(MP) =y=lagax a =x4- Ju'u"dx → inu tK n-STEPSWHERE MEN AREFUNCTIONS.(CONVERSIONSNOT DERIVATIVES)Pn MWHICH INTEGRAL?1) MAKE IT2) FIND U; CREATE U'3) WE HAVE4) MAKE IT LOOK LIKE TEMPLATE5) PERFORM INTEGRALPRETTY:WE WANT.CHANGE OF BASE:y=loga x -LogX= In xlogaDEFINITE INTEGRALSALSOUnay=Sax'dx = afx*axy=S(ax^+bx") dxFa) = ffondxJHondk = FO = F(b) - F(a)"dx%3D%3D

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Answered: Find the derivative of y = In{(7x³ + 4)…

Math

Calculus

Find the derivative of y = In{(7x³ + 4) V3x + 10}

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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Question

I really need help figuring out how to do this problem, using the cheat sheet formula provided

c) Find the derivative of y = In{(7x3 + 4) V3x + 10}

*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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