Tentukan f’(x) jika 1) f(x) = (x2+4×4-6)(3×2+4×3) 2) f(x)=(x-3+6×2)/(x4+3×2+7x)

NOMOR 1.

f(x) = (x² + 4x⁴ – 6)(3x² + 4x³)

Misalkan,

u(x) = (x² + 4x⁴ – 6) >>>>>>>>> u'(x) = (2x + 16x³)

v(x) = (3x² + 4x³) >>>>>>>>>>> v'(x) = (6x + 12x²)

Maka,

f'(x) = u'(x)•v(x) + u(x)•v'(x)

f'(x) = (2x + 16x³)•(3x² + 4x³) + (x² + 4x⁴ – 6)•(6x + 12x²)

f'(x) = (6x³ + 8x⁴ + 48x⁵ + 64x⁶) + (6x³ + 12x⁴ + 24x⁵ + 48x⁶ – 36x – 72x²)

f'(x) = (64x⁶ + 48x⁵ + 8x⁴ + 6x³) + (48x⁶ + 24x⁵ + 12x⁴ + 6x³ – 72x² – 36x)

f'(x) = 64x⁶ + 48x⁶ + 48x⁵ + 24x⁵ + 8x⁴ + 12x⁴ + 6x³ + 6x³ – 72x² – 36x

f'(x) = 112x⁶ + 72x⁵ + 20x⁴ + 12x³ – 72x² – 36x

NOMOR 2.

f(x) = (x³ + 6x²)/(x⁴ + 3x² + 7x)

Misalkan,

u(x) = (x³ + 6x²) >>>>>>>>>>> u'(x) = (3x² + 12x)

v(x) = (x⁴ + 3x² + 7x) >>>>>>> v'(x) = (4x³ + 6x + 7)

Maka,

f'(x) = [u'(x)•v(x) – u(x)•v'(x)] / v²(x)

f'(x) = [(3x² + 12x)•(x⁴ + 3x² + 7x) – (x³ + 6x²)•(4x³ + 6x + 7)] / (x⁴ + 3x² + 7x)²

f'(x) = [(3x⁶ + 9x⁴ + 21x³ + 12x⁵ + 36x³ + 84x²) – (4x⁶ + 6x⁴ + 7x³ + 24x⁵ + 36x³ + 42x²)] / (x⁴ + 3x² + 7x)²

f'(x) = [(3x⁶ + 12x⁵ + 9x⁴ + 21x³ + 36x³ + 84x²) – (4x⁶ + 24x⁵ + 6x⁴ + 7x³ + 36x³ + 42x²)] / (x⁴ + 3x² + 7x)²

f'(x) = [(3x⁶ + 12x⁵ + 9x⁴ + 57x³ + 84x²) – (4x⁶ + 24x⁵ + 6x⁴ + 43x³ + 42x²)] / (x⁴ + 3x² + 7x)²

f'(x) = (84x² – 42x² + 57x³ – 43x³ + 9x⁴ – 6x⁴ + 12x⁵ – 24x⁵ + 3x⁶ – 4x⁶) / (x⁴ + 3x² + 7x)²

f'(x) = (42x² + 14x³ + 3x⁴ – 12x⁵ – x⁶) / (x⁴ + 3x² + 7x)²