derivative of (arctan(5x)^2)

Lösung

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

\frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

2 arctan (5 x) \frac{d}{d x} (arctan (5 x))

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

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= 2 arctan (5 x) \frac{5}{25 x ^{2} + 1}

Vereinfache

2 arctan (5 x) \frac{5}{25 x ^{2} + 1} : \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

= \frac{10 arctan ( 5 x )}{25 x ^{2} + 1}

\int \frac{x ^{4} + 8 x ^{2} + 8}{x ^{3} - 4 x} d x

t a y l or x^{3} - 3 x^{2} + 5 x - 7, 0

s l o p e (1.7) (3.3)

\int_{0}^{2} \frac{d t}{4 + t ^{2}} d x

y^{^{''}} + 49 y = 0, y (0) = 4, y^{^{'}} (0) = - 6