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Beliebt Rechnen >

derivative of log_{10}(cos(x))

Lösung

\frac{d}{d x} (lo g_{10} (cos (x)))

Lösung

- \frac{tan ( x )}{ln ( 10 )}

Schritte zur Lösung

\frac{d}{d x} (lo g_{10} (cos (x)))

Wende die log Regel an:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( cos ( x ) )}{ln ( 10 )})

Entferne die Konstante:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (cos (x)))

Wende die Kettenregel an:

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

= \frac{1}{cos ( x )} \frac{d}{d x} (cos (x))

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

= \frac{1}{ln ( 10 )} \cdot \frac{1}{cos ( x )} (- sin (x))

Vereinfache

\frac{1}{ln ( 10 )} \cdot \frac{1}{cos ( x )} (- sin (x)) : - \frac{tan ( x )}{ln ( 10 )}

= - \frac{tan ( x )}{ln ( 10 )}

Graph

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\int x^{14} e^{x^{15}} d x

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