Tentukan turunan fungsi berikut

1. y = (4x + 3)⁵

y'=  5.4 (4x+ 3)⁴

y'= 20 (4x+ 3)⁴

2. g = 3(x² – x + 2)–10

g' = 3(2x- 1)

g'= 6x – 3

3. f(x) = (3x² – 5)⁴

f'(x)=  4. 6x. (3x² -5)³

f'(x)=  24x (3x² -5)³

4. g(x) = (4x − 2)(3x + 4)

g'(x)= 4(3x+4)+ 3(4x-2)

g'(x) = 12x +16 +12x – 6

g'(x) = 24x +10

5. f(x) = (3x² – 2)(4x – 1)​

f'(x) = 6x (4x- 1) + 4(3x² -2)

f'(x) =  24x² -6x + 12 x² -8

f'(x) = 36x² – 6x – 8

Penjelasan dengan langkah-langkah:

1. y = (4x + 3)5

u(x) = 4x + 3

u'(x) = 4

y' = u'(x) k

y' = (4)5

y' = 20

2. g(x) = 3(x² – x + 2) – 10

u(x) = x² – x + 2

u'(x) = 2x – 1

v(x) = – 10

v'(x) = 0

g'(x) = k{u'(x)} + v'(x)

g'(x) = 3(2x – 1) + 0

g'(x) = 6x – 3

3. f(x) = (3x² – 5)4

u(x) = 3x² – 5

u'(x) = 6x

f'(x) = {u'(x)}k

f'(x) = (6x)4

f'(x) = 24x

4. g(x) = (4x – 2)(3x + 4)

u(x) = 4x – 2

u'(x) = 4

v(x) = 3x + 4

v'(x) = 3

g'(x) = u'(x) . v(x) + v'(x) . u(x)

g'(x) = 4(3x + 4) + 3(4x – 2)

g'(x) = 12x + 16 + 12x – 6

g'(x) = 24x + 10

5. f(x) = (3x² – 2)(4x – 1)

u(x) = 3x² – 2

u'(x) = 6x

v(x) = 4x – 1

v'(x) = 4

f'(x) = u'(x) . v(x) + v'(x) . u(x)

f'(x) = 6x(4x – 1) + 4(3x² – 2)

f'(x) = 24x² – 6x + 12x² – 8

f'(x) = 36x² – 6x – 8