derivative ln(Ax^4+B)

解

導関数

ln (A x^{4} + B)

\frac{4 A x ^{3}}{A x ^{4} + B}

解答ステップ

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

連鎖法則を適用:

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

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

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

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

簡素化

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

= \frac{4 A x ^{3}}{A x ^{4} + B}