derivative 2arcsin(x^3)

Lösung

ableitung von

2 arcsin (x^{3})

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \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}

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

Vereinfache

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

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

\frac{d}{d x} (10 e^{- 2 x})

d er i v a t i v e h (t) = (t + 5)^{\frac{2}{3}} (3 t^{2} - 5)^{3}

x \to 9 lim (\frac{5}{( x - 9 )})

7 y y^{^{'}} = x

x \to (a + 1) lim (x^{2} - 1)