найдите значение производной функции f(x)=6cos x +2sin x при х= пи/4. Created by vasilevaul99. algebra-ru

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July 2022 2 33 Report

найдите значение производной функции f(x)=6cos x +2sin x при х= пи/4

csharp

f(x) = 6cosx + 2sinx, x₀ = π/4

f'(x) = -6sinx + 2cosx

f'(x₀) = f'(π/4) = -6sin(π/4) + 2cos(π/4) = -6 · √2/2 + 2 · √2/2 = -3√2 + √2 = -2√2

-2√2

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teledima00

$f(x) = 6cos(x)+ 2sin(x)$

Найдём производную f'(x)

$f'(x) = (6cos(x)+2sin(x))' = (6cos(x))'+(2sin(x))' = -6sin(x) + 2cos(x)$

Подставим в f'(x) x = π/4

$f'(\frac{\pi}{4}) = -6sin\frac{\pi}{4} + 2cos\frac{\pi}{4}= -6\cdot \frac{\sqrt2}{2} + 2\cdot \frac{\sqrt2}{2} = -4\frac{\sqrt2}{2} = -2\sqrt2$

Ответ: $-2\sqrt2$

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