215.- Найдите производную функции: a) f (x) = x³-3x ; 1+4x5 6) f (x) =(3+x²) (2-√x); B) f (x) = 5-2x6 ; 1-x8 r) f (x) = √x (3x5 - x).

Решение: a) f(x) = (x³-3x)/(1+4x⁵) f'(x) = ((3x²-3)(1+4x⁵) - (x³-3x)(20x⁴))/(1+4x⁵)² = (3x² + 12x⁷ - 3 - 12x⁵ - 20x⁷ + 60x⁵)/(1+4x⁵)² = (-8x⁷ + 48x⁵ + 3x² - 3)/(1+4x⁵)² б) f(x) = ((3/x)+x²) (2-√x) f'(x) = ((-3/x²)+2x)(2-√x) + ((3/x)+x²)(-1/(2√x)) = (-6/x² + (3√x)/x² + 4x - 2x√x) + (-3/(2x√x) - x²/(2√x)) = (-6/x² + 3√x/x² + 4x - 2x√x - 3/(2x√x) - x²/(2√x)) в) f(x) = (5-2x⁶)/(1-x⁸) f'(x) = ((-12x⁵)(1-x⁸) - (5-2x⁶)(-8x⁷))/(1-x⁸)² = (-12x⁵ + 12x¹³ + 40x⁷ - 16x¹³)/(1-x⁸)² = (-4x¹³ + 40x⁷ - 12x⁵)/(1-x⁸)² г) f(x) = √x (3x⁵ - x) f'(x) = (1/(2√x)) (3x⁵ - x) + √x (15x⁴ - 1) = (3x⁵ - x)/(2√x) + (15x⁴√x - √x) = (3x⁵ - x + 30x⁵ - 2x)/(2√x) = (33x⁵ - 3x)/(2√x) Ответ: a) f'(x) = (-8x⁷ + 48x⁵ + 3x² - 3)/(1+4x⁵)² б) f'(x) = (-6/x² + 3√x/x² + 4x - 2x√x - 3/(2x√x) - x²/(2√x)) в) f'(x) = (-4x¹³ + 40x⁷ - 12x⁵)/(1-x⁸)² г) f'(x) = (33x⁵ - 3x)/(2√x)