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Beliebt Rechnen >

derivative of 4arcsin(x^3)

Lösung

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

Lösung

\frac{12 x ^{2}}{1 - x ^{6}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

\frac{1}{1 - ( x ^{3} ) ^{2}} \frac{d}{d x} (x^{3})

= \frac{1}{1 - ( x ^{3} ) ^{2}} \frac{d}{d x} (x^{3})

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

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

Vereinfache

4 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{12 x ^{2}}{1 - x ^{6}}

= \frac{12 x ^{2}}{1 - x ^{6}}

Graph

Beliebte Beispiele

derivative 2/(\sqrt[3]{x^2)}

d er i v a t i v e \frac{2}{3 x ^{2}}

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\frac{d}{d x} (\frac{4 csc ( x )}{5 ^{x}})

limit as x approaches infinity of n/(n!)

x \to \infty lim (\frac{n}{n !})

derivative ln(49sin^2(x))

d er i v a t i v e ln (49 sin^{2} (x))

(\partial)/(\partial v)(v^2)

\frac{\partial}{\partial v} (v^{2})