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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

\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}

Vereinfache

\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}

a re a y = 10 x, y = x^{2} - 11, x

x^{^{''}} + 2 x^{^{'}} + 2 x = 2

\frac{d}{d x} (- 2 ln (cos (x)))

\int x \cdot e^{2 x^{2}} d x

\int_{1}^{2} - x^{2} + 3 x - 2 d x