derivative of 1/2 cos^4(5x)

Lösung

\frac{d}{d x} (\frac{1}{2} cos^{4} (5 x))

- 10 cos^{3} (5 x) sin (5 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} cos^{4} (5 x))

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (cos^{4} (5 x))

Wende die Kettenregel an:

4 (cos (5 x))^{3} \frac{d}{d x} (cos (5 x))

= 4 (cos (5 x))^{3} \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{2} \cdot 4 (cos (5 x))^{3} (- sin (5 x) \cdot 5)

Vereinfache

\frac{1}{2} \cdot 4 cos^{3} (5 x) (- sin (5 x) \cdot 5) : - 10 cos^{3} (5 x) sin (5 x)

= - 10 cos^{3} (5 x) sin (5 x)

\frac{d}{d y} (1 - x^{2} y)

n \to \infty lim (9)

\frac{d}{d x} (- 12 x^{2} - 16 x + 16)

\frac{d}{d x} (x^{\frac{9}{10}})

\frac{d P}{d t} + 2 tP = P + 4 t - 2