derivative of sqrt(cos(5x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

\int \frac{x ^{2} - 4 x + 3}{x ^{3} + 2 x ^{2} + x} d x

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