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1 a d = a + a+ (a ), e d = e, sin d = cos, (af() + bg())d = a d = log, cosd = sin, f()d + b g()d d 3 d
2 d d d d d d ( )d ( + )d ( 3 )d (e )d
3 ( sin 3 cos)d g ()f (g())d = f(g()) e d e d ( )e d cos d sin d e cose d 3
4 + d + d e e + d cos sin d 3 f(g())g ()d = f(t)dt, t = g(), dt = g ()d + d e e + d sin (cos + ) d
5 cos 5 d sin cos cos + d d e + d f()g ()d = f()g() f ()g()d e d log d log d sin d 5
6 e d cosd 5 F() = b f()d = F(b) F(a) [f()] b a a ( + )d d 9 d e d π sin d 6
7 π cos d π sin d e d + d π cos sin d π 6 b f(g())g ()d = g(b) a β α f(t)dt, t = g(), α = g(a), β = + d e e + d 7
8 π sin (cos + ) d π cos 5 d 7 b b f()g ()d = [f()g()] b a f ()g()d a a e d e log d 8 a d = a + a+ (a ), e d = e, sin d = cos, (af() + bg())d = a d = log, cosd = sin, f()d + b g()d d 8
9 d = + + = 3 d 3 d = = d d = log d d = d = + + = = d d = d = + + = 3 3 = 3 9
10 d d = d = + + = d d = 3 d = = d d = 3 3 d = = = ( )d ( )d = ( + )d
11 ( + )d = + log ( 3 )d ( 3 )d = ( 3 )d = log + 3 = log + 3 (e )d (e )d = e log ( sin 3 cos)d ( sin 3 cos)d = cos 3 sin
12 9 g ()f (g())d = f(g()) e d e d = () e d = e e d e d = ( ) e d = e ( )e d ( )e d = ( ) e d = e cos d
13 cos d = () cos d = sin sin d sin d = ( ) sin d = cos e cose d e cos e d = (e ) cos e d = sin e + d ( + ) + d = d = log d + d = ( + ) + d = log + 3
14 e e + d e (e e + d = + ) e + d = log(e + ) cos sin d cos sin d = (sin ) d = log sin sin f(g())g ()d = f(t)dt, t = g(), dt = g ()d + d t = + dt = d + d = t dt = + + = t = + t
15 e e + d t = e + dt = e d e e + d = t dt = + + = 3 t t = ( + ) + 3 t sin (cos + ) d t = cos + dt = sin d sin (cos + ) d = t ( dt) = t3 + )3 = (cos 3 3 cos 5 d t = sin dt = cosd cos 5 d = cos( sin ) d = ( t ) dt = ( t + t )dt = t 3 t3 + 5 t5 = t( 3 t + 5 t ) = sin ( 3 sin + 5 sin ) sin cos cos + d t = cos + dt = cossin d sin cos cos + d = t dt = log t = log(cos + ) 5
16 d t = = t, d = tdt d = ( t )t( tdt) = (t t )dt = ( t5 5 t3 3 ) = t3 (3t 5) 5 = ( )(3( ) 5) 5 = ( )(3 + ) 5 e + d t = e + dt = e d, d = t dt e + d = t t dt = ( t )dt = log t log t t = log e log(e + ) = log(e + ) e + d = + e e d = e + ( e e + )d = log(e + ) f()g ()d = f()g() f ()g()d 6
17 e d e d = (e ) d = e e d = e e = ( )e log d log d = d = log ( ) log d = log d = log = ( log ) log d log d = () log d = log d = log = (log ) sin d sin d = ( cos ) d = ( cos) ( cos )d = cos + 7
18 sin e d e d = (e ) d = e e d = e (e ) d = e (e e d) = e e + e = e ( + ) cosd cosd = (sin ) d = sin sin d = sin ( cos ) d = sin (( cos ) = sin + cos sin = ( ) sin + cos ( cos)d) b F() = f()d = F(b) F(a) a [f()] b a 8
19 ( + )d ( + )d = [ ] = ( = 3 ) ( ) = d d = 3 d = [ 5 5 ] = 5 ()5 = 5 5 = d 9 d = 9 d = [ ] 9 = 9 = 6 = 5 e d e d = [e ] = e e = e 9
20 π sin d π sin d = [ cos] π = cos π + cos = + = π cos d π cosd = [sin ] π = sin π sin = = π sin d π sin d = [ cos ] π = cos π + cos = + = e d e d = [ e ] = e e = e
21 + d + d = [ log( + )] = log log log = π cos sin d π π π cos sin d = [log sin ] π π = log = log = log sin π log sin π = log log 3 b f(g())g ()d = g(b) a β α f(t)dt, t = g(), α = g(a), β = + d t = + dt = d = t = =
22 t = + d = t dt = [ + + ] t = [ t] = e e + d t = e + dt = e d = t = = t = e + e e+ e + d = t dt = [ + + ] e+ = [ 3 t t] e+ t = 3 ((e + ) e + ) π sin (cos + ) d t = cos + dt = sin d = t = = π t = π sin (cos + ) d = t ( dt) = [ t3 3 ] = 3 ( 8) = 7 3 π cos 5 d t = sin dt = cos d = t = = π t =
23 π cos 5 d = π cos ( sin ) d = = [t 3 t3 + 5 t5 ] = ( ) = 8 5 ( t ) dt = ( t +t )dt b b f()g ()d = [f()g()] b a f ()g()d a a e d e ) = e d = (e ) d = [e ] e d = e [e ] = e (e e log d e log d = e = e (e ) = e () log d = [ log ] e d = e log e log []e 3
9 5 ( α+ ) = (α + ) α (log ) = α d = α C d = log + C C 5. () d = 4 d = C = C = 3 + C 3 () d = d = C = C = 3 + C 3 =
5 5. 5.. A II f() f() F () f() F () = f() C (F () + C) = F () = f() F () + C f() F () G() f() G () = F () 39 G() = F () + C C f() F () f() F () + C C f() f() d f() f() C f() f() F () = f() f() f() d =
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2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
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九州大学学術情報リポジトリ Kyushu University Institutional Repository 物理工科のための数学入門 : 数学の深い理解をめざして 御手洗, 修九州大学応用力学研究所 QUEST : 推進委員 藤本, 邦昭東海大学基盤工学部電気電子情報工学科 : 教授 http://hdl.handle.net/34/500390 出版情報 : バージョン :accepted
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