derivative ln(x^3+5x+3)

解

導関数

ln (x^{3} + 5 x + 3)

\frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

解答ステップ

\frac{d}{d x} (ln (x^{3} + 5 x + 3))

連鎖法則を適用:

\frac{1}{x ^{3} + 5 x + 3} \frac{d}{d x} (x^{3} + 5 x + 3)

= \frac{1}{x ^{3} + 5 x + 3} \frac{d}{d x} (x^{3} + 5 x + 3)

\frac{d}{d x} (x^{3} + 5 x + 3) = 3 x^{2} + 5

= \frac{1}{x ^{3} + 5 x + 3} (3 x^{2} + 5)

簡素化

\frac{1}{x ^{3} + 5 x + 3} (3 x^{2} + 5) : \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}

= \frac{3 x ^{2} + 5}{x ^{3} + 5 x + 3}