derivative of 6arcsin(x^4)

Lösung

\frac{d}{d x} (6 arcsin (x^{4}))

\frac{24 x ^{3}}{1 - x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (6 arcsin (x^{4}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (arcsin (x^{4}))

Wende die Kettenregel an:

\frac{1}{1 - ( x ^{4} ) ^{2}} \frac{d}{d x} (x^{4})

= \frac{1}{1 - ( x ^{4} ) ^{2}} \frac{d}{d x} (x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

= 6 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3}

Vereinfache

6 \cdot \frac{1}{1 - ( x ^{4} ) ^{2}} \cdot 4 x^{3} : \frac{24 x ^{3}}{1 - x ^{8}}

= \frac{24 x ^{3}}{1 - x ^{8}}

\frac{d y}{d x} = x + 5 y, y (0) = 3

x \to 0 lim (cos^{\frac{3}{x ^{2}}} (2 x))

\frac{d y}{d x} = y^{2}

d er i v a t i v e f (x) = \frac{6}{3 x + 1}, at a = - 1

\int \frac{x}{1 + x} d x