Question

найдите производные .................

Answer 1

Используемые правила:

(const)' = 0

(xⁿ)' = n*xⁿ⁻¹

(sin x)' = cos x

(u/v)' = (u'v - uv') / v²

1) y = 3x⁴ - 4/x² + 10

y' = (3x⁴ - 4/x² + 10)' = (3x⁴)' - (4 * x⁻²)' + (10)'

// (3x⁴)' = 12x³; (4 * x⁻²)' = -8 * x⁻3 = - 8/x³; (10)' = 0;

y' = 12x³ + 8/x³

2) y = sin 3x

y' = (sin 3x)'

y' = 3 * cos 3x

3) y = 6 * x / (1 + x²)

y' = 6 * (x' * (1 + x²) - x * (1 + x²)' ) / (1 + x²)² = (1 * (1 + x²) - x * 2 * x) / (1 + x²)²

y' = -12 * x² / (1 + x²)² + 6 / (1 + x²)