derivative of 1/4 sin^4(x)

Lösung

\frac{d}{d x} (\frac{1}{4} sin^{4} (x))

sin^{3} (x) cos (x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{4} sin^{4} (x))

Entferne die Konstante:

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

= \frac{1}{4} \frac{d}{d x} (sin^{4} (x))

Wende die Kettenregel an:

4 (sin (x))^{3} \frac{d}{d x} (sin (x))

= 4 (sin (x))^{3} \frac{d}{d x} (sin (x))

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

= \frac{1}{4} \cdot 4 (sin (x))^{3} cos (x)

Vereinfache

\frac{1}{4} \cdot 4 sin^{3} (x) cos (x) : sin^{3} (x) cos (x)

= sin^{3} (x) cos (x)

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

t an g e n t y = x^{2} - 1, (5, 24)

\frac{d}{d x} (x^{5} \cdot ln (x))

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

n = 0 \sum \infty \frac{1}{3 ^{n - 1}}