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人気のある微分積分 >

derivative (-1)/(sqrt(10+4t^2))

解

導関数

\frac{- 1}{10 + 4 t ^{2}}

解

\frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

解答ステップ

\frac{d}{d t} (\frac{- 1}{10 + 4 t ^{2}})

簡素化

\frac{- 1}{10 + 4 t ^{2}} : - \frac{1}{10 + 4 t ^{2}}

= \frac{d}{d t} (- \frac{1}{10 + 4 t ^{2}})

定数を除去:

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

= - \frac{d}{d t} (\frac{1}{10 + 4 t ^{2}})

指数の規則を適用する:

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

= - \frac{d}{d t} ((10 + 4 t^{2})^{- \frac{1}{2}})

連鎖法則を適用:

- \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (10 + 4 t^{2})

= - \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \frac{d}{d t} (10 + 4 t^{2})

\frac{d}{d t} (10 + 4 t^{2}) = 8 t

= - (- \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \cdot 8 t)

簡素化

- (- \frac{1}{2 ( 10 + 4 t ^{2} ) ^{\frac{3}{2}}} \cdot 8 t) : \frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

= \frac{4 t}{( 10 + 4 t ^{2} ) ^{\frac{3}{2}}}

グラフ

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