TUGAS MATEMATIKA 1

DISUSUN

Oleh :

Nama : Muhammad Wahyu UtamaProdi : Teknik ElektronikaKelas : 1 EASemester : 2 (Genap)

POLITEKNIK MANUFAKTUR NEGERI BANGKA BELITUNGTAHUN AJARAN 2014/2015

Kawasan Industri Air Kantung Sungailiat, Bangka 33211Telp. (0717) 93586, Fax. (0717) 93585Email : polman@polman-babel.ac.id

Carilah nilai turunan dari fungsi berikut ini.

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=x+ x

73

y '=1+ 73x

73−3

3=1+ 73x

43

y '=1+ 73

3√x4

4. y= 2

x12

+ 6

x32

=2 x−12 +6 x

−32

y '=2.−12. x

−12 −2

2+6.−32. x

−32 −2

2=−x−32 −9x

−52 =−1

x32

− 9

x52

y '= −1√ x3

− 9√ x5

5. u=x2→u '=2 xv=sin 2x→v '=2. cos xy '=u' . v+u . v '=2 x . 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 '=2 x .cos3 x+ (x2+1 ) .−3.sin 3 xy '=2x .cos 3 x+(−3 x2−3 ) . sin 3 x

7. u=sin 5x→u'=5.cos5 xv=tan 2 x→v '=2. sec 22 xy '=u' . v+u . v '=5. cos5 x . tan 2 x+sin 5 x .2 . sec2 2xy '=5. cos5 x . tan 2 x+2.sin 5 x . sec22 x

8. u=cos3 x→u'=−3. sin 3xv=cot 4 x→v '=−4.csc2 4 xy '=u' . v+u . v '=−3. sin 3 x .cot 4 x+cos3 x .−4.csc2 4 xy '=−3. sin 3 x .cot 4 x−4.cos3 x . csc2 4 x

9. u=sin 5x→u'=5.cos5 xv=cos7 x→ v'=−7.sin 7 x

y '=u' . v−u . v '

v2 =5. cos5 x .cos7 x−sin 5 x .−7. sin7 x¿¿¿

y '=5.cos 5x .cos7 x+7. sin 5 x . sin 7 xcos27 x

10. u=cos6 x→u'=−6. sin 6 xv=tan 2 x→v '=2. sec 22 x

y '=u' . v−u . v '

v2 =−6. sin 6 x . tan2 x−cos6 x .2. sec22 x¿¿¿

y '=−6. sin 6x . tan 2x−2.cos 6 x . sec2 2xtan22 x