Question

Tentukan turunan fungsi berikut ! a)f(x)=4x³-5x²+sin3x
B)f(x)=(4x+1) X cos5x
C) f(x)=x²+3x+2/x²-4
D)f(x)=(tg(2x²))pngkat5

Pakek jalan yak

Answer 1

Verified answer

Turunan

a.
f(x)= 4x³ - 5x² + sin 3x
f ' (x) = 3(4)(x)² - 5(2)(x) + 3 cos 3x
f '(x) = 12 x² - 10x + 3 cos x

b.
f(x)= (4x+1)(cos 5x)
u = 4x + 1 --> u' = 4
v = cos 5x --> v' = - 5 sin 5x
f' (x) = u'v + uv'
f'(x) = 4(cos 5x) + (4x+1)(- 5 sin 5x)
f '(x) = 4 cos 5x - 20x sin 5x  - 5 sin 5x

c)
f(x)= x²+3x + 2) /x²-4
f(x) = (x+2)(x+1)/ (x+2)(x-2)
f(x) = (x+1)/(x-2)
f= u/v
u = x + 1 --> u' = 1
v = x - 2 --> v' = 1
f '=  u' v - u v ' / v²
f ' (x) = {1(x-2) - (x+1)(1)} / (x -2)²
f '(x) =  {x - 2 - x - 1} /(x-2)²
f '(x) = -3/(x-2)²
.
d.
y = tan⁵ (2x²)
u = 2x²
du/dx = 4x

v = tan u
dv/du = sec² u

y = v⁵
dy/dv = 5v⁴

dy/dx = dy/dv. dv/du. du/dx
f'(x) = 5v⁴. sec² u. (4x)
f '(x)  = 5(tan⁴ u) (sec² 2x²)(4x)
f' (x) = 5 tan⁴ 2x² . sec² 2x²  . 4x
f'(x)= 20 x . tan⁴ (2x²). sec² (2x²)