Question

Tentukan Turunan Pertama Fungsi Berikut​

Answer 1

4

[tex]f(x) = \frac{6}{ {x}^{5} } - \frac{12}{5 {x}^{3} } [/tex]

[tex]f(x) = 6 {x}^{ - 5} - \frac{12 {x}^{ - 3} }{5} [/tex]

turunan pertama

[tex]f'(x) = ( - 5) \times 6 {x}^{ - 5 - 1} - ( - 3) \times \frac{12 {x}^{ - 3 - 1} }{5} \\ [/tex]

[tex]f'(x) = - 30 {x}^{ - 6} + \frac{36 {x}^{ - 4} }{5} [/tex]

[tex]f'(x) = - \frac{ 30}{ {x}^{6} } + \frac{36}{5 {x}^{4} } [/tex]

5

[tex]f(x) = (4x -1)(5x + 2)[/tex]

[tex]f(x) = 20 {x}^{2} + 3x - 2[/tex]

turunan pertama

[tex]f'(x) =2 \times 20 {x}^{2 - 1} + 1 \times 3 {x}^{1 - 1} - 0 \\ [/tex]

[tex]f'(x) =40x + 3[/tex]

6

[tex]f(x) = (4 {x}^{5} + 3) {}^{7} [/tex]

turunan pertama

[tex]f'(x) =7 \times (4 {x}^{5} + 3) {}^{7 - 1} \times 20 {x}^{4} [/tex]

[tex]f'(x) =140 {x}^{4} (4 {x}^{5} + 3) {}^{6} [/tex]

7

[tex]f(x) = \frac{5x + 2}{3x - 4} [/tex]

u = 5x + 2

u' = 5

v = 3x - 2

v' = 3

turunan pertama

[tex]f'(x) = \frac{u'v - uv'}{ {v}^{2} } [/tex]

[tex]f'(x) = \frac{(5)(3x - 2) - (5x + 2)(3)}{(3x - 2) {}^{2} } [/tex]

[tex]f'(x) = \frac{(15x - 10) - (15x + 6)}{(3x -2) {}^{2} } [/tex]

[tex]f'(x) = \frac{ - 16}{(3x - 2) {}^{2} } [/tex]