derivative f(x)=2sin^4(sqrt(x))

Lösung

ableitung von

f (x) = 2 sin^{4} (x)

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

Schritte zur Lösung

\frac{d}{d x} (2 sin^{4} (x))

Entferne die Konstante:

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

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

= 2 \cdot 4 (sin (x))^{3} \frac{cos ( x )}{2 x}

Vereinfache

2 \cdot 4 sin^{3} (x) \frac{cos ( x )}{2 x} : \frac{4 sin ^{3} ( x ) cos ( x )}{x}

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

\int x^{2} + e^{x} d x

t an g e n t y = \frac{x}{8 x - 4}, at x = 2

s \to 1 lim (\frac{s ^{3} - 1}{s - 1})

\int_{- \infty}^{0} (x e^{2 x}) d x

\frac{d}{d x} (cos^{4} (3 x^{2}))