derivative of 5cos(6ln(x))

Lösung

\frac{d}{d x} (5 cos (6 ln (x)))

- \frac{30 sin ( 6 ln ( x ) )}{x}

Schritte zur Lösung

\frac{d}{d x} (5 cos (6 ln (x)))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (cos (6 ln (x)))

Wende die Kettenregel an:

- sin (6 ln (x)) \frac{d}{d x} (6 ln (x))

= - sin (6 ln (x)) \frac{d}{d x} (6 ln (x))

\frac{d}{d x} (6 ln (x)) = \frac{6}{x}

= 5 (- sin (6 ln (x)) \frac{6}{x})

Vereinfache

5 (- sin (6 ln (x)) \frac{6}{x}) : - \frac{30 sin ( 6 ln ( x ) )}{x}

= - \frac{30 sin ( 6 ln ( x ) )}{x}

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