derivative f(x)=ln(6x^3+e^x)

解

導関数

f (x) = ln (6 x^{3} + e^{x})

\frac{18 x ^{2} + e ^{x}}{6 x ^{3} + e ^{x}}

解答ステップ

\frac{d}{d x} (ln (6 x^{3} + e^{x}))

連鎖法則を適用:

\frac{1}{6 x ^{3} + e ^{x}} \frac{d}{d x} (6 x^{3} + e^{x})

= \frac{1}{6 x ^{3} + e ^{x}} \frac{d}{d x} (6 x^{3} + e^{x})

\frac{d}{d x} (6 x^{3} + e^{x}) = 18 x^{2} + e^{x}

= \frac{1}{6 x ^{3} + e ^{x}} (18 x^{2} + e^{x})

簡素化

\frac{1}{6 x ^{3} + e ^{x}} (18 x^{2} + e^{x}) : \frac{18 x ^{2} + e ^{x}}{6 x ^{3} + e ^{x}}

= \frac{18 x ^{2} + e ^{x}}{6 x ^{3} + e ^{x}}