derivative 2\sqrt[4]{9-x^2}

解

導関数

2 4 9 - x^{2}

- \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

解答ステップ

\frac{d}{d x} (2 4 9 - x^{2})

定数を除去:

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

= 2 \frac{d}{d x} (4 9 - x^{2})

連鎖法則を適用:

\frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

= \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - 2 x

= 2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x)

簡素化

2 \cdot \frac{1}{4 ( 9 - x ^{2} ) ^{\frac{3}{4}}} (- 2 x) : - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}

= - \frac{x}{( 9 - x ^{2} ) ^{\frac{3}{4}}}