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Beliebt Rechnen >

derivative of 3ln(cos(x))

Lösung

\frac{d}{d x} (3 ln (cos (x)))

Lösung

- 3 tan (x)

Schritte zur Lösung

\frac{d}{d x} (3 ln (cos (x)))

Entferne die Konstante:

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

= 3 \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)

= 3 \cdot \frac{1}{cos ( x )} (- sin (x))

Vereinfache

3 \cdot \frac{1}{cos ( x )} (- sin (x)) : - 3 tan (x)

= - 3 tan (x)

Graph

Beliebte Beispiele

laplacetransform 6-6e^{-5t}

l a pl a ce t r an s f or m 6 - 6 e^{- 5 t}

integral from 0 to 5/12 of 60x

\int_{0}^{\frac{5}{12}} 60 x d x

derivative of e^{2x}-e^2

\frac{d}{d x} (e^{2 x} - e^{2})

maclaurin (1+x)^{-3/5}

ma c l a u r in (1 + x)^{- \frac{3}{5}}

limit as x approaches 7 of (x+7)/(|x+7|)

x \to 7 lim (\frac{x + 7}{∣ x + 7 ∣})