Question

1 и 2 задание за 50б

Answer 1

1)

y = sqrt(x) * (1 + x^2) = x^0.5 + x^2.5

y' = 0.5*x^(-0.5) + 2.5*x^1.5

при x = 1 y' = 0.5 * 1 + 2.5 * 1 = 3

2)

a)

$f(x) = frac{2x-1}{2x+1} = 1 - frac{2}{2x + 1}$

$f'(x) = 0 - frac{-2*2}{(2x + 1)^2} = frac{4}{(2x + 1)^2}$

б)

$f(x) = frac{1 + cos x}{sin x}$

$f'(x) = frac{-sin(x)*sin(x) - cos(x)(1 + cos(x))}{sin^2x} = frac{-sin^2(x) - cos^2(x) - cos(x)}{sin^2(x)} = frac{-1 - cos(x)}{sin^2(x)}$