tugas 1 matematika 2
TRANSCRIPT
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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
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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
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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