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人気のある微分積分 >

derivative g(x)=((pi^2))/(x^2+4x)

解

導関数

g (x) = \frac{( π ^{2} )}{x ^{2} + 4 x}

解

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

解答ステップ

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

定数を除去:

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

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

指数の規則を適用する:

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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

グラフ

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