derivative of 3arcsin(x^3)

Lösung

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

\frac{9 x ^{2}}{1 - x ^{6}}

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \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}

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

Vereinfache

3 \cdot \frac{1}{1 - ( x ^{3} ) ^{2}} \cdot 3 x^{2} : \frac{9 x ^{2}}{1 - x ^{6}}

= \frac{9 x ^{2}}{1 - x ^{6}}

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

\int \frac{3 x ^{2} - 2}{x ^{2} - 4 x - 12} d x

s l o p e y = x

\frac{\partial}{\partial w} (x e^{w})

\int_{0}^{6} x 36 - x^{2} d x