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# TCTC - Mat 140 - Class Notes - Week 3

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TCTC - Mat 140 - Class Notes - Week 3

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##### Description: Unit 2- Chapter 3, Sections 1-3 Notes and Practice Problems (worked out and with answers)
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Unformatted text preview: Lgwat (2+ 3+x7c Section 3.2 Product and Quotient ROLS f,g both di Aferentiablo EfCV)(X)]' = f(X)g'(x) g(x) f'X) f(x) 1.9 (XIF'(X)-f(X)g'(x) 92(x) Examplo D)-f(x) = ex (x3-4x23x) f'(x) -ex(3x2-3x+2)+(x3-4x +2x)ex ex- [3x -8x+2+X3 -4x2+2x] = e *(x3-x2-Cox+2) (t)= 3J - Exam po 2) (4) Att 'l) = 1 3et 3+2/3 V (+)-(tet)(\) 4 + ctct tet) Et c'p ter ( 4te) - 4et-tet tet 1264 ex-133-7-L0X42) terk proclock (401) 14a+D lu a2 +4a+40/ facturing. Optionitby 4*et*c* : - * ( 41 +44 ) -- (42) w +2e2 t2e24 +22 Exampo 3) 6 (X) =(217= (2+3)(2+) G'(X) = (2 + x y2)+(2+ 2) FES-)+(3-X) = 2 Exampo 4) Find the tangent Rino y text Co2) (Ite* )04)-(style (409) - (1+x)ex ( [tex)? (1 +Y= -finx y=Sinx y'-(OSX FFFFFFFFFFBEE GEDE dx d (SinX) = COSX Cd (COS X) = -Sinx d. ctanx) = Sec2x) d (cotx) = -csc2x ) Prove di canx) dx (Six) COS XYCOS X) sinxe-Sinx) Cos2X COS2x Sin2x = = sec2x (86 sa Heg. COS2X (082x As you (sec ) -cecxtanxa 3 (CSC) = -CSG XCOTX d. (secx)= q (eds) Cos (0)-1(-sin CDS 2X - Sinx = | SINX-secx COS2X COSX COSX 4anxPg. 196 2) fcx)=x COS X +2tan X F'(x) = X(-Sinx) (COX) I+2sec2x = -XSINX +COSX + 2sec 2x 10) y=SINO COSO y'=Sinol-Sinet COSD-COSE = COS -S NZO = COS 28 14 yasint (tant)(cost) -Sint (sec2t) lttant sint (It tant)? = COST (COSE tant)-(Sint (sec2x) COSE Sint .sect T + tant ) 2 N' = Cost Sint - tantsect (lt tants 0 fct) = tetcott ft):(tct)(-csc2t) +cott Ytet tet). Fet (-tesc2t+t cott + Cott) product Ruta 52 d (xsin x) *x cosx+sinx d"=-XSinxtcosx+cosx = -XS N X2lox dX35 d'' E-XCDSX-35sinx

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