Tugas 6 deferensial

Tugas 6
1.

Tentukan derivasi pertama dari fungsi berikut:
a. f(x) = 4,
=0
b. f(x) = 3x,
=3
c. f(x) = 2x2 +1,
= 4x
d. f(x) = x3 + 5,
= 3x²
e. f(x) = 4x
=

2.

x

¼

+ 4.

−3
4

Hitung dy/dx dari persamaan berikut:
a. y = 5 + 2x + 3x2 – 4x3,
= -12x²+6x+2
b. y = x4 + 4x + 5,
= 4x³+4
c. y = (x-1)(x+2).
= x²+2x-x-2
= 2x²+1
d. y = (x+2)/(x2-1)
= (x+2)(x²-1)
= x³-x+2x²-2
= x³+2x²-x-2
= 3x²+4x-3

e. y =

3.

1
x −3
2

'

=

U V −UV '
V²

= 2X+1

Tentukan derivasi pertama dan ke dua dari fungsi berikut:

a. y = e 4x,
y’ = U’×e⁴

=

ax

4e

y’’ =
y’’ =

4.
16 e

4e
4x

4x

b. y = 3e-2x
y’ = −2 . 3 e−2 x
= −6 e2 x

=
c. Hitung nilai derivasi masing-masing bila x =0.
X=0
a. y’ = 4e4(0) = 4
y” = 16e4(0) = 16

b. y’ = -6e-2(0) = -6
y” = 12e-2(0) = 12

4. a. y = In4x
Y’ =

U'
U

=

4
4x

=

1
x

Y” = -x-2

b. y = 2In 7x
U'
U

y’ =

= 2(

7
1
) = 2(
)=
7x

x

c. jika x = 1
1
x

=

1
1

=1

-x-2 = -(1)-2
=-

1
12

= -1

5. dik TC = 3Q2 + 7Q + 12

2
x

dC
dQ

Hit = MC =
AC =

TC
Q

=(

= 6Q + 7
2

3 Q 7 Q+12
= 3Q + 7 +
+
Q
Q

12
Q

= 3.3 + 7 + 4 = 9 + 7 + 4

= 20



Q=3
TC = 3(3)2+7(3)+12
= 27 + 21 + 12
= 60
TC 60

=
AC =
= 20
Q
3
MC = 6 x 3 + 7
= 25
3
48
Q+4 +
2
8

7. AC =

TC = AC x Q
3
46
Q+4 + ¿ x Q
2

8

=(
=
MC =

3
2

Q2 + 4Q +46

dTC
dQ

= 3Q + 4

8. a. TC = FC + VC

VC = AVC.Q
1

= ( 2+ Q¿ Q
2

= 50 + VC
= 50 + 20Q +
MC = TC’
MC = 2 + Q

1
2

Q2

= 2Q +

1
2

Q2

b. TC = 50 + 2Q +

1
2

Q2
1
2

Q20 = 50 + 2(20) +

(20)2

= 50 + 40 + 200
= 290
Q22 = 50 + 2(22) +

1
2

(20)2

= 50 + 40 + 200
= 336
336 – 290 = 46

9. C = 0,03y2 + 0,1y + 30
MPC = C’
= 0,06y + 0,1
(y = 5) = (0,06 x 5 ) + 0,1
= 0,30 + 0,1
= 0,4

MPS = 1 – MPC
= 1 – 0,4
= 0,6

MR =

dTR
dQ