Question

Помогите с производными по матеше​

Answer 1

Ответ:

• a) y = 4x³ =4×3=13+3=16x

Answer 2

Используемые правила:

1) (xⁿ)' = nxⁿ⁻¹

2) (x + y)' = x' + y'

3) (const)' = 0

4) (u/v)' = (u'v - uv')/v²

а) y = 4x³ => y' = 3*4 *x³⁻¹ = 12x²

б) y = x² + 5 => y' = (x²)' + 5' = 2x + 0 = 2x

в) y = x²(2x + 8) => y' = 2x³ + 8x² = (2x³)' + (8x²)' = 6x² + 16x = 2x(3x² + 8)

г) ↓
$y = \frac{x^{2}}{2x+1} => y' = \frac{(x^2)'(2x+1) - x^{2}(2x + 1)'}{(2x+1)^{2}} = \frac{2x(2x + 1) - 2x^{2}}{(2x+1)^{2}} = \frac{2x(2x+1)}{(2x+1)^{2}} - \frac{2x^{2}}{(2x+1)^{2}} =\\\\\\=\frac{2x}{2x +1} - \frac{2x^{2}}{(2x+1)^{2}}$

д) y = 4x³ - 3x² - x - 1 => y' = (4x³)' - (3x²)' - (x)' - (1)' = 12x² - 6x - 1

x₀ = -1

=> y(x₀) = 12*(-1)² - 6*(-1) - 1 = 12 + 6 - 1 = 17