Question

plis bantu jawab kak butuh sekarang nomor 1,3 dan 5​

Answer 1

Jawaban:

1. f(x) = sin 2x + cos 3x

f'(x)= 2 cos 2x - 3 sin 3x

f'(π/2) = 2 cos π - 3 sin 3/2 π

f'(π/2) = 2 (-1) -3(-1) = -2+ 3

f'(π/2) =1

2. Jawaban:

a)45x^2 + 34x + 1

b)3x^2 + 36x + 5 / x^2 + 12x + 36

Penjelasan dengan langkah-langkah:

a) f(x) = (3x+1)(5x^2 + 4x - 1)

u v

bentuk f(x) = U.V → f'(x) = u'v + uv'

u = 3x+1

v = 5x^2 + 4x - 1

u' = 3

v' = 10x + 4

f'(x) = 3(5x^2+4x-1) + (3x+1)(10x+4)

= 15x^2 + 12x - 3 + (30x^2 + 12x + 10x + 4)

= 45x^2 + 34x + 1

Dengan Perkalian(cara 2):

f(x) = 3x(5x^2 + 4x - 1) + 5x^2 + 4x - 1

= 15x^3 + 12x^2 - 3x + 5x^2 + 4x - 1

= 15x^3 + 17x^2 + x - 1

f'(x) = 45x^2 + 34x + 1

b) f(x) = 3x^2-5/x+6

bentuk f(x) = u/v → f'(x) = u'v - uv'/v^2

u = 3x^2 - 5

v = x + 6

u' = 6x

v' = 1

f'(x) = 6x(x+6) - (3x^2-5)1 / (x+6)^2

= 6x^2 + 36x - (3x^2-5) / (x+6)^2

= 3x^2 + 36x + 5 / x^2 + 12x + 36