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

Lösung

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

- \frac{5 sin ( 10 x )}{2}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

2 cos (5 x) \frac{d}{d x} (cos (5 x))

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

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

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

Vereinfache

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

= - \frac{5 sin ( 10 x )}{2}

\frac{d}{d x} (tan (3 x - x^{2}))

\frac{d y}{d x} = \frac{1}{x sin ( y ) + 2 sin ( 2 y )}

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

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\int 54 sec^{4} (x) d x