derivative of (5sqrt(1-x^3)/6)

Lösung

\frac{d}{d x} (\frac{5 1 - x ^{3}}{6})

- \frac{5 x ^{2}}{4 - x ^{3} + 1}

Schritte zur Lösung

\frac{d}{d x} (\frac{5 1 - x ^{3}}{6})

Entferne die Konstante:

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

= \frac{5}{6} \frac{d}{d x} (1 - x^{3})

Wende die Kettenregel an:

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

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

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

= \frac{5}{6} \cdot \frac{1}{2 1 - x ^{3}} (- 3 x^{2})

Vereinfache

\frac{5}{6} \cdot \frac{1}{2 1 - x ^{3}} (- 3 x^{2}) : - \frac{5 x ^{2}}{4 - x ^{3} + 1}

= - \frac{5 x ^{2}}{4 - x ^{3} + 1}

\int 13 arctan (x) d x

x \to + 0 lim (\frac{e ^{2 x} - 1}{sin ( 3 x )})

x \to 3 lim (x^{3} - 2 x^{2} + 1)

n = 1 \sum \infty \frac{30}{3 ^{n}}

a re a y = \frac{2}{1 + x ^{2}}, y = ∣ x ∣