derivative of arctan(9^x)

解

\frac{d}{d x} (arctan (9^{x}))

\frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}

解答ステップ

\frac{d}{d x} (arctan (9^{x}))

連鎖法則を適用:

\frac{1}{( 9 ^{x} ) ^{2} + 1} \frac{d}{d x} (9^{x})

= \frac{1}{( 9 ^{x} ) ^{2} + 1} \frac{d}{d x} (9^{x})

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

= \frac{1}{( 9 ^{x} ) ^{2} + 1} \cdot 2 ln (3) \cdot 9^{x}

簡素化

\frac{1}{( 9 ^{x} ) ^{2} + 1} \cdot 2 ln (3) \cdot 9^{x} : \frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}

= \frac{2 ln ( 3 ) \cdot 9 ^{x}}{8 1 ^{x} + 1}