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人気のある微分積分 >

derivative of (4+8xcosh(2x))

解

\frac{d}{d x} ((4 + 8 x) cosh (2 x))

解

8 cosh (2 x) + sinh (2 x) \cdot 2 (4 + 8 x)

解答ステップ

\frac{d}{d x} ((4 + 8 x) cosh (2 x))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 4 + 8 x, g = cosh (2 x)

= \frac{d}{d x} (4 + 8 x) cosh (2 x) + \frac{d}{d x} (cosh (2 x)) (4 + 8 x)

\frac{d}{d x} (4 + 8 x) = 8

\frac{d}{d x} (cosh (2 x)) = sinh (2 x) \cdot 2

= 8 cosh (2 x) + sinh (2 x) \cdot 2 (4 + 8 x)

グラフ

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