Jadikan Jawaban Terbaik dan Tercerdas ☺️

1. f ( x ) = 6 => f ' ( x )

Rumus :

f ' ( x ) = n . × ^ n - 1

Maka f ' ( x ) = 1 . 6 × ^ 1 - 1

6 × ^ 0 = 6 . 1

Maka f ' ( x ) = 6

2. f ( x ) = 5 x => f ' ( x )

Rumus :

f ' ( x ) = n . × ^ n - 1

Maka f ' ( x ) = 1 . 5 × ^ 1 - 1

5 × ^ 0 = 5 . 1

Maka f ' ( x ) = 5

3. f ( x ) = 3 x ² => f ' ( x )

f ' ( x ) = 3 x ²

f ' ( x ) = 2 . 3 x ²

f ' ( x ) = 6 x ²

4. f ( x ) = 5 x ² - 2 x ³ + 5 x - 4 => f ' ( x )

f ' ( x ) = 5 x ² - 2 x ³ + 5 x - 4

f ' ( x ) = 5 x ² - 2 x ³ + - 9

f ' ( x ) = 25 - 8 + - 9

f ' ( x ) = 8 x

5. f ( x ) = ( 3 x + 2 ) ( 2 x - 5 ) => f ' ( x )

Rumus:

f ( x ) = u v -> f ( x ) ' = U ' V + V ' U

Jadi:

f ( x ) = ( 3 x +2 ) ( 2 x - 5 )

f ( x ) ' = U ' V + V ' U

f ( x ) ' = 3 ( 2 x - 5 ) + 2 ( 3 x + 2 )

f ( x ) ' = 6 x - 15 + 6 x + 4

f ( x ) ' = 6 x + 6 x - 15 +

f ( x ) ' = 12 x - 11

6. f ( x ) = 5 x + 1 => f ' ( x )

------------

2 x - 5

f ( x ) = 5 x + 1

------------

2 x - 5

y = 5 x + 1

-----------

2 x - 5

y ( x - 5 ) = 5 x + 1

y x - 5 y = 5 x + 1

y x - 5 x = 1 + 5 y

x ( y - 5 ) = 5 y - 1

x = 5 y - 1

----------

y - 5

x = - 5 y + 2 => f -¹ ( x ) = - 5 x + 2

------------- --------------

- y + 5 - x + 2

7. f ( x ) = ( 3 x + 2 ) ⁸ => f ' ( x )

f ( x ) = ( 3 x + 2 ) ⁸

f ( x ) = 24 x + 2

f ( x ) = 48 x