Question

Ребят , помогите пожалуйста.

Answer 1

1. Δf = f(x) - f(x₀)

f(x) = x²,

x₀ = 2,

f(x₀) = x₀² = 2² = 4,

Δf = x² - 4.

2.

а) f(x) = x² + x⁵ + x⁷,

f'(x) = (x² + x⁵ + x⁷)' = 2x + 5x⁴ + 7x⁶.

б) f(x) = (x-3)/(x-2),

$f'(x) = (\frac{x-3}{x-2})' = \frac{(x-3)'(x-2)-(x-3)(x-2)'}{(x-2)^2} =$

$= \frac{x-2 - (x-3)}{(x-2)^2} = \frac{x-2 - x + 3}{(x-2)^2} = \frac{1}{(x-2)^2}$

3.

f(x) = (x-7)¹⁰,

f'(x) = ((x-7)¹⁰)' = 10·(x-7)⁹·(x-7)' = 10·(x-7)⁹.

4.

h(x) = f(g(x)),

$h'(x) = f'(y|_{y=g(x)})\cdot g'(x)$

или

$h'(x) = f'_g(g(x))\cdot g'_x(x)$