derivative of (sin^2(x)^2)

Lösung

\frac{d}{d x} ((sin^{2} (x))^{2})

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

Schritte zur Lösung

\frac{d}{d x} ((sin^{2} (x))^{2})

Vereinfache

(sin^{2} (x))^{2} : sin^{4} (x)

= \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)

= 4 (sin (x))^{3} cos (x)

Vereinfache

= 4 sin^{3} (x) cos (x)

\int sin (6 x) cos (2 x) d x

\int cos^{4} (7 - x) sin (7 - x) d x

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

n = 0 \sum \infty \frac{1}{n ^{2} + 2 n}

\int \frac{5000 x}{25 x + 1500} d x