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Unformatted text preview: 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. Section 3.7 Derivatives of Inverse Functions and Logarithms 151 211115)( _1) : _ _ ln(l+€1n3) dy w 1 1 y—log3(1+61n3)— 1113 : E—(fi)(1+_e—1n 3)(1“3)= 1+61n3 1 1_1n_x M _'n_X 2M~3ELX I_ 3 y: og4x+ og4x2 In + In — 1114+ 1n4 ‘ 1114 i y — x1n4 _ _ xlne I ~ x lnx 1 /_ y ‘103256x —log5\/; 11125 _ 211:5 _ 21n5 21n5 “ (2ln5)(x—1nx) :> y —( _ _ lnr l _ l2 d _ 1 2| Y—logzr'10g4r"(r)(£—')-W :‘ ax [m](21nr>(:): m _ w lnr l~ lnzr d _, 1 _ Zlnr y —10g3 r- 1°g9 r * (T)(1:—r):(1n3)(1n9) :> 31 ' [(1n3)1(ln9)] (2 1n r) (F) — r(ln 3)(ln9) ,3 1n x+1'"3 (ln3)ln :f‘ y=1°g3(<:t1)")'= (1;. 2 .S 1)=1n11i11=1n<x+1>—1n<x—1> d ._ 1 1 —2 :> a¥_X+1—x—1:(x+1)(x—l) x (In51/2 7x _ 7x Ins _ 7x (MSW _ ”(fi) _ 1 5 ln(3xi2) 1 y — IOgS (3x+2) — 1°g5 (3x+2) — 11.5 * (HT) ln5 — 51n( _ 1 _ 1 91 _ L 3 _ (3x+2)~3x 1 — 21n7x 2 1n (3x+2) _> dx 2-7x 2-(3x+2) — 2x(3x+2) — x(3x+2) . . d . y : 651n(log7 6) : 051n(%) 2)» d—Z = sin(—g) +0 [cos (%)] (91:7) 2 sm(10g7 6)+ 1% cos(log7 6) 1n 2) _ 10 (sin6c059)__ln(Sin9)+ln(COS(’)-Ines—1n2'9 _1n(sin9)+1n(c059)—9—61n2 y- g7 e”2a _ ln7 _ ln7 Q): W 0056 _ sin19 1 13; d9 (sin6)(1n 7) (cos 19)(ln 7) ln7 ln7 — (1:117) (COW [21116 1 ~— x — ln_e‘ — _X- I _ 1 y log5e 1n5 lnS ‘5 y In5 —1 x292 w111xz+1ne2—1nz—1n x+1_ 21nx+2—1n2—lln(x+1) y— 0g; 2§7x+1 ”‘ ln2 — ln2 :> I _2-__1___4(§+U_'X:_fl. y— .7 x1n2 2(ln2)(x+1) 2x(x+1)(ln2) 2x(x+1)1n2 - I _ | 12 d _ 1 ) 12 l _1 1 y H 30s21_ 3(n()/(n) :> 33% _ [3(nt/(n )(ln 3)] (”112) __ 7 (log 3)3og2| y: 310%? (10g; 0 " flfi‘g—t): W A 71% M (1‘35) [am/[(1:12)] (11.112) — t(lnl)3(ln8) 2m y=log2 (8t‘"2)=fl#=mi—SZM=3+W : 9.1% y : tlog3 (6(Sin‘)(l"3)) = TLfi—y—t) — might) : “Sing?“ 3) — t sint —> 31% — sin t +tcost y=(x+1)x :> lny=1n(x+1)x:x]n(x+1):> §=1n(x+1)+x.(xil) : y/:(x+1)x[x:] yzxml) =>1ny=1nx"‘“)=(x+1)lnx 2) §=1nx+(x+1)(%)=lnx+1+% =>y’=x X“ (1 +— i+1nx) +1n(x+ 1)] ...
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