derivative 4arcsin(x^3)

Lösung

ableitung von

4 arcsin (x^{3})

\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}}

\int_{0}^{2} (x 9 - x^{2}) d x

\int (3 x - 5)^{2} d x

n = 1 \sum \infty \frac{1}{n ^{1.1}}

\int \frac{7}{6 + 7 x} d x

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