derivative 8sin^4(sqrt(x))

Lösung

ableitung von

8 sin^{4} (x)

\frac{16 sin ^{3} ( x ) cos ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} (8 sin^{4} (x))

Entferne die Konstante:

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

= 8 \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}

= 8 \cdot 4 (sin (x))^{3} \frac{cos ( x )}{2 x}

Vereinfache

8 \cdot 4 sin^{3} (x) \frac{cos ( x )}{2 x} : \frac{16 sin ^{3} ( x ) cos ( x )}{x}

= \frac{16 sin ^{3} ( x ) cos ( x )}{x}

\frac{d}{d x} (e^{x^{2} s i n (x)})

\int \frac{a}{3 x ^{2}} d x

t an g e n t f (x) = 11 - x^{2}

l a pl a ce t r an s f or m 40

x \to 4 π lim (e^{t a n (x)})