derivative of ln(x^3+4)

解

\frac{d}{d x} (ln (x^{3} + 4))

\frac{3 x ^{2}}{x ^{3} + 4}

解答ステップ

\frac{d}{d x} (ln (x^{3} + 4))

連鎖法則を適用:

\frac{1}{x ^{3} + 4} \frac{d}{d x} (x^{3} + 4)

= \frac{1}{x ^{3} + 4} \frac{d}{d x} (x^{3} + 4)

\frac{d}{d x} (x^{3} + 4) = 3 x^{2}

= \frac{1}{x ^{3} + 4} \cdot 3 x^{2}

簡素化

\frac{1}{x ^{3} + 4} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + 4}

= \frac{3 x ^{2}}{x ^{3} + 4}