1.Soal:
f(x)=5x2-7x+6,Tentukan f’(x) dengan cara,
a.Pendekatan Limit
b.Turunan Langsung
Penyelesaian:
a.Pendekatan Limit
f (x)=5x2-7x+6
f ’(x) =lim h=0
f(x+h)-f(x)/h
=lim h=0
5(x+h)2-(7(x+h))+6-(5x2-7x+6)/h
=lim h=0 5(x2=2xh+h2)-(7x+7h)+6-(5x2-7x+6)/h
=lim h=0 5x2+10xh+5h2-7x-7h+6-5x2+7x-6/h
=lim h=0 10xh+5h2-7h/h
=lim h=0 h(10x+5h-7)/h
=lim h=0 10x+5h-7 ;karna h=0
=10x-7
b.Turunan Langsung
f(x)=5x2-7x+6
f ‘(x)=a.nx2-1
f ’(x)=5.2x2-1-7.1x1-1
=10x-7
2. a. f (x) = (x² - 3) (x –
7)
g(x) h(x)
g¹(x) = 2x
h¹(x) = 1
f¹(x) = g¹(x) . h(x) + g(x) . h¹(x)
= 2x² (x – 7) + (x² - 3) 1
= 2x² - 14x + x² - 3
= 3x² - 14x – 3
b. f (x) = 2x² - 3
x² - 4
g(x) = 2x² - 3 h(x) = x² - 4
g¹(x) = 4x h¹(x) = 2x
f¹(x) = g¹(x) .
(h(x) – g(x) . h¹(x)
(h
(x))²
= 4x (x² - 4) – (2x² - 3) 2x
(x² - 4)²
= 4x³ - 16x – (4x³ - 6x)
x⁴ - 8x² + 16
= 4x³ - 16x – 4x³ + 6x
x⁴ - 8x² + 16
= - 16x + 6x
x⁴ - 8x² + 16
= - 10 x
x⁴ - 8x² + 16
3. Dik :
f (x) = x² - 5
G (x) = x² +
2
H (x) = x +
3
Jawab :
a. (gof) (x) = go (x² - 5)
= x² + 2
= (x² - 5)² + 2
= x⁴ - 10x² + 25 + 2
= x⁴ - 10x² + 27
b. (fog) (x) = fo (x² + 2)
= x² - 5
= (x² + 2)² - 5
= x⁴ + 4x² + 4 – 5
= x⁴ + 4x² - 1
c. (foh) (x) = fo (x + 3)
= x² - 5
=
(x + 3)² - 5
=
x² + 6x + 9 – 5
=
x² + 6x + 4
d. (gofo) (x) = (gof) (h(x))
= (gof) (x + 3)
= g {(x + 3)² - 5}
= g (x² + 6x + 9 – 5)
= g (x² + 6x + 4)
= x² + 2
= (x² + 6x + 4)² + 2
= (x² + 6x + 4) (x² + 6x + 4) + 2
= x⁴ + 6x³ + 4x² + 6x³ + 36x² + 24x + 4x² + 24x + 16 + 2
= x⁴ + 12x³ + 44x² + 48x + 18
Kalo kurang Jelas Download Di SINI
*typo* no 2.A riv bawah g¹(x) . h(x) + g(x) . h¹(x)
BalasHapus= 2x (x – 7) + (x² - 3) 1
Hayo yg blum ngerjain segera kerjain, sambil copas, sambil di pelajarin caranya...
BalasHapus