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人気のある微分積分 >

derivative y= 4/x+sqrt(x+0.5)-5x

解

導関数

y = \frac{4}{x} + x + 0.5 - 5 x

解

- \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

解答ステップ

\frac{d}{d x} (\frac{4}{x} + x + 0.5 - 5 x)

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (x + 0.5) - \frac{d}{d x} (5 x)

\frac{d}{d x} (\frac{4}{x}) = - \frac{4}{x ^{2}}

\frac{d}{d x} (x + 0.5) = \frac{0.5}{x + 0.5}

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

= - \frac{4}{x ^{2}} + \frac{0.5}{x + 0.5} - 5

グラフ

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