2x^4+16x д) f(x) = x3 - 12x + 36x + 1 Тема таблица производных, производная....

chertik1 @chertik1

July 2022 1 7 Report

а) f(x) = x^2-6x+5 при х0 = 2

б) f(x) = sinx при х0 = - П/2

в) f(x) = 3/x при х0 = -1

г) f(x) = 1/2x^4+16x

д) f(x) = x3 - 12x + 36x + 1

Тема таблица производных, производная.. кто может подробно зделать зарание благодарю

Answers & Comments

Vladislav006

Verified answer

A)
$f'(x) = (x^2-6x+5)' = (x^2)' - (6x)' +5' = 2x-6 \\ \\ f'(x_0) = f'(2) = 2*2-6 = -2$

б)
$f'(x) = (sinx)' = cosx \\ \\ f'(x_0) = f'(- \frac{ \pi }{2} ) = cos(- \frac{ \pi}{2} ) = 0$

в)
$f'(x) = (3/x)' = (3x^{-1})' = 3 * (-1) * x^{-1-1} = -\frac{3}{x^{2} } \\ \\ f'(x_0) = f'(-1) = -\frac{3}{(-1)^{2} } = -3$

г)
$f'(x) = (1/2x^4+16x)' = (\frac{1}{2} x^{4})' + (16x)' = \frac{1}{2} * 4 *x^3 + 16= \\ \\ = 2x^3 + 16$

д)
$f'(x) = (x^3 - 12x + 36x + 1)' = (x^3)' - (12x)' + (36x)' + 1' = \\ \\ = 3 x^{2} -12 + 36 = 3 x^{2} +24$

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