derivative of arctan(ln(4x^5))

解

\frac{d}{d x} (arctan (ln (4) x^{5}))

\frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}

解答ステップ

\frac{d}{d x} (arctan (ln (4) x^{5}))

簡素化

arctan (ln (4) x^{5}) : arctan (2 ln (2) x^{5})

= \frac{d}{d x} (arctan (2 ln (2) x^{5}))

連鎖法則を適用:

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

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

\frac{d}{d x} (2 ln (2) x^{5}) = 10 ln (2) x^{4}

= \frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \cdot 10 ln (2) x^{4}

簡素化

\frac{1}{( 2 ln ( 2 ) x ^{5} ) ^{2} + 1} \cdot 10 ln (2) x^{4} : \frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}

= \frac{10 ln ( 2 ) x ^{4}}{4 ln ^{2} ( 2 ) x ^{10} + 1}