1) f(x) = (x2+4x4-6)(3x2+4x3)
2) f(x)=(x-3+6x2)/(x4+3x2+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
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