derivative y=ln(5+2x+x^3)

解

導関数

y = ln (5 + 2 x + x^{3})

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

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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