derivative of 8sin^6(sqrt(x))

Lösung

\frac{d}{d x} (8 sin^{6} (x))

\frac{24 sin ^{5} ( x ) cos ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (8 sin^{6} (x))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (sin^{6} (x))

Wende die Kettenregel an:

6 (sin (x))^{5} \frac{d}{d x} (sin (x))

= 6 (sin (x))^{5} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = \frac{cos ( x )}{2 x}

= 8 \cdot 6 (sin (x))^{5} \frac{cos ( x )}{2 x}

Vereinfache

8 \cdot 6 sin^{5} (x) \frac{cos ( x )}{2 x} : \frac{24 sin ^{5} ( x ) cos ( x )}{x}

= \frac{24 sin ^{5} ( x ) cos ( x )}{x}

n = 3 \sum \infty \frac{1}{2 ^{n}}

\int \frac{m}{e ^{a x}} d x

x \to 0 lim (x csc (x))

\int e^{3 x} (e^{3 x} - 8)^{5} d x

x \to 4 lim (g (x))