derivative ln(1+4^x)

解

導関数

ln (1 + 4^{x})

\frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}

解答ステップ

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

連鎖法則を適用:

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

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

\frac{d}{d x} (1 + 4^{x}) = ln (2) \cdot 2^{2 x + 1}

= \frac{1}{1 + 4 ^{x}} ln (2) \cdot 2^{2 x + 1}

簡素化

\frac{1}{1 + 4 ^{x}} ln (2) \cdot 2^{2 x + 1} : \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}

= \frac{ln ( 2 ) \cdot 2 ^{2 x + 1}}{1 + 4 ^{x}}