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人気のある微分積分 >

derivative (35)/(4+x+sqrt(x))

解

導関数

\frac{35}{4 + x + x}

解

- \frac{35 ( 1 + 2 x )}{2 x ( 4 + x + x ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{35}{4 + x + x})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 35 \frac{d}{d x} (\frac{1}{4 + x + x})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= 35 \frac{d}{d x} ((4 + x + x)^{- 1})

連鎖法則を適用:

- \frac{1}{( 4 + x + x ) ^{2}} \frac{d}{d x} (4 + x + x)

= - \frac{1}{( 4 + x + x ) ^{2}} \frac{d}{d x} (4 + x + x)

\frac{d}{d x} (4 + x + x) = \frac{1}{2 x} + 1

= 35 (- \frac{1}{( 4 + x + x ) ^{2}} (\frac{1}{2 x} + 1))

簡素化

35 (- \frac{1}{( 4 + x + x ) ^{2}} (\frac{1}{2 x} + 1)) : - \frac{35 ( 1 + 2 x )}{2 x ( 4 + x + x ) ^{2}}

= - \frac{35 ( 1 + 2 x )}{2 x ( 4 + x + x ) ^{2}}

グラフ

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