derivative of (x+3/(|x+3|))

解

\frac{d}{d x} (\frac{x + 3}{∣ x + 3 ∣})

0

解答ステップ

\frac{d}{d x} (\frac{x + 3}{∣ x + 3 ∣})

商の法則を適用:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x + 3 ) ∣ x + 3 ∣ - \frac{d}{d x} ( ∣ x + 3 ∣ ) ( x + 3 )}{∣ x + 3 ∣ ^{2}}

\frac{d}{d x} (x + 3) = 1

\frac{d}{d x} (∣ x + 3 ∣) = \frac{x + 3}{∣ x + 3 ∣}

= \frac{1 \cdot ∣ x + 3 ∣ - \frac{x + 3}{∣ x + 3 ∣} ( x + 3 )}{∣ x + 3 ∣ ^{2}}

簡素化

\frac{1 \cdot ∣ x + 3 ∣ - \frac{x + 3}{∣ x + 3 ∣} ( x + 3 )}{∣ x + 3 ∣ ^{2}} : 0

= 0