Question

Tolong bantu yaa ????

(1). Jika f(x) = 3x pangkat 3 akar x + 9x kuadrat - 5, maka f'(x) = ? (2). Carilah differensial dari : y = - 4cos (2x + 3). ? (3). F(x) = sin ( 3x - 30 ), hitunglah f'(pi per 3) ? (4). Hitunglah f'(x) dari persamaan f(x) = 5x kuadrat di kali cos 2x

Answer 1

1.) f(x) = 3x³√x + 9x² - 5
=> f(x) =
=> f'(x) =
=> f'(x) = (21/2)x²√x + 18x
2.) y = -4cos(2x + 3)
Gunakan aturan rantai,
=> y' = -4*(2x+3)'*[cos(2x+3)']
=> y' = -4*2*-sin(2x+3)
=> y' = 8sin(2x + 3)
3.) f(x) = sin(3x - 30°)
=> f'(x) = 3 cos(3x - 30°).
=>
=>
4.) f(x) = 5x²cos2x
=> Misalkan u(x) = 5x² dan v(x) = cos2x.
=> u'(x) = 10x dan v'(x) = -2sin2x.
=> f'(x) = u'(x)v(x) + u(x)v'(x)
=> f'(x) = 10xcos2x - 10x²sin2x
=> f'(x) = 10x(cos2x - xsin2x)