derivative of sqrt(\sqrt{1+\sqrt{x)}+1}

解

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

\frac{1}{8 x 1 + x + 1 x + 1}

解答ステップ

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

連鎖法則を適用:

\frac{1}{2 1 + x + 1} \frac{d}{d x} (1 + x + 1)

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

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

= \frac{1}{2 1 + x + 1} \cdot \frac{1}{4 x x + 1}

簡素化

\frac{1}{2 1 + x + 1} \cdot \frac{1}{4 x x + 1} : \frac{1}{8 x 1 + x + 1 x + 1}

= \frac{1}{8 x 1 + x + 1 x + 1}