簡約 1/21/2 (16-x^2)^{-1/2}(2x)

解

簡約

\frac{1}{2} \cdot \frac{1}{2} (16 - x^{2})^{- \frac{1}{2}} \cdot (2 x)

\frac{x}{2 ( - x ^{2} + 16 ) ^{\frac{1}{2}}}

解答ステップ

\frac{1}{2} \cdot \frac{1}{2} (16 - x^{2})^{- \frac{1}{2}} (2 x)

指数の規則を適用する:

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

= 2 \cdot \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{( - x ^{2} + 16 ) ^{\frac{1}{2}}} x

分数を乗じる:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 1 \cdot 2 x}{2 \cdot 2 ( 16 - x ^{2} ) ^{\frac{1}{2}}}

共通因数を約分する:

2

= \frac{1 \cdot 1 \cdot 1 \cdot x}{2 ( 16 - x ^{2} ) ^{\frac{1}{2}}}

乗算:

1 \cdot 1 \cdot 1 \cdot x = x

= \frac{x}{2 ( - x ^{2} + 16 ) ^{\frac{1}{2}}}