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人気のある微分積分 >

derivative f(x)=(3x+1)(5x+4)

解

導関数

f (x) = (3 x + 1) (5 x + 4)

解

30 x + 17

解答ステップ

\frac{d}{d x} ((3 x + 1) (5 x + 4))

積の法則を適用:

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

f = 3 x + 1, g = 5 x + 4

= \frac{d}{d x} (3 x + 1) (5 x + 4) + \frac{d}{d x} (5 x + 4) (3 x + 1)

\frac{d}{d x} (3 x + 1) = 3

\frac{d}{d x} (5 x + 4) = 5

= 3 (5 x + 4) + 5 (3 x + 1)

簡素化

3 (5 x + 4) + 5 (3 x + 1) : 30 x + 17

= 30 x + 17

グラフ

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