derivative of ln((x^2^2))

解

\frac{d}{d x} (ln ((x^{2})^{2}))

\frac{4}{x}

解答ステップ

\frac{d}{d x} (ln ((x^{2})^{2}))

簡素化

ln ((x^{2})^{2}) : ln (x^{4})

= \frac{d}{d x} (ln (x^{4}))

連鎖法則を適用:

\frac{1}{x ^{4}} \frac{d}{d x} (x^{4})

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

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{1}{x ^{4}} \cdot 4 x^{3}

簡素化

\frac{1}{x ^{4}} \cdot 4 x^{3} : \frac{4}{x}

= \frac{4}{x}