tugas 1 matematika 2

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TUGAS 1 MATEMATIKA 2 Nama : Cinjy Saylendra Monica Prodi : Teknik Elektronika Kelas : 1E A Semester : 2 (Dua) Tahun Ajaran : 2014/2015 Soal : 1. y=x 7 + 6 x 5 +12 x 3 2. y=x 5 +2 x 3 +3 x 7 3. y= x 2 + 3 x 7 4. y= 2 x + 6 x 3 5. y=x 2 . sin 2 x 6. y=( x 2 +1 ) . cos3 x 7. y=sin5 x. tan2 x 8. y=cos3 x. cot4 x 9. y= sin5 x cos7 x 10. y= cos6 x tan2 x Jawaban : 1. y ' =7 x 6 +30 x 4 + 36x 2

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Page 1: Tugas 1 Matematika 2

TUGAS 1MATEMATIKA 2

Nama : Cinjy Saylendra MonicaProdi : Teknik ElektronikaKelas : 1E ASemester : 2 (Dua)Tahun Ajaran : 2014/2015

Soal :

1. y=x7+6 x5+12x3

2. y=x−5+2 x−3+3 x−7

3. y=√x2+ 3√ x7

4. y= 2

√ x+ 6

√x3

5. y=x2 . sin2 x

6. y=( x2+1 ) .cos3 x

7. y=sin5 x . tan 2x

8. y=cos3 x .cot 4 x

9. y= sin 5 xcos7 x

10. y= cos6 xtan 2 x

Jawaban :

1. y '=7 x6+30 x4+36 x2

2. y '=−5 x−6−6 x−4−21 x−8

3. y=x22+x

73

y=x+x73

Page 2: Tugas 1 Matematika 2

y '=1+ 73x73−33=1+ 7

3x43

y '=1+ 733√x4

4. y= 2

x12

+ 6

x32

y=2x−12 +6 x

−32

y '=2.−12. x

−12

−22+6.−3

2. x

−32

−22

y '=−x−32 −9 x

−52 =−1

x32

− 9

x52

y '= −1

√ x3− 9

√ x5

5. u=x2→u '=2xv=sin 2x→v '=2. cos xy '=u' . v+u . v '

y '=2x .sin 2 x+x2.2 .cos xy '=2x .sin 2 x+2x2 .cos x

6. u=x2+1→u '=2xv=cos3 x→ v '=−3.sin 3 xy '=u' . v+u . v '

y '=2x .cos 3x+(x2+1 ) .−3. sin 3 xy '=2x .cos 3x+(−3x2−3 ). sin 3 x

7. u=sin 5x→u '=5.cos 5xv=tan 2 x→v '=2. sec22 xy '=u' . v+u . v '

y '=5. cos5 x . tan 2x+sin 5 x .2 . sec22xy '=5. cos5 x . tan2 x+2. sin5 x . sec22x

8. u=cos3 x→u'=−3. sin 3 xv=cot 4 x→v '=−4.csc24 xy '=u' . v+u . v '

y '=−3.sin 3 x .cot 4 x+cos3 x .−4.csc24 xy '=−3. sin 3 x .cot 4 x−4. cos3 x .csc 24 x

Page 3: Tugas 1 Matematika 2

9. u=sin 5x→u '=5.cos 5xv=cos7 x→v '=−7. sin7 x

y '=u' . v−u . v '

v2

y '=5. cos5 x .cos7 x−sin5 x .−7. sin 7 x¿¿¿

y '=5.cos 5x .cos7 x+7.sin 5 x .sin 7 xcos27x

10. u=cos6 x→u'=−6. sin 6 xv=tan 2 x→v '=2. sec22 x

y '=u' . v−u . v '

v2

y '=−6. sin 6 x . tan 2x−cos 6 x .2. sec22x¿¿¿

y '=−6. sin 6 x . tan 2 x−2. cos6 x . sec22 xtan22x