derivative of 5ln(cos(x))

Lösung

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

- 5 tan (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

= 5 \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)

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

Vereinfache

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

= - 5 tan (x)

x \to 0 lim (2 (\frac{a ^{x} - 1}{x}))

\int_{1}^{12} \frac{1}{x - 10} d x

\frac{\partial}{\partial x} (\frac{e ^{x}}{x ^{2} + 10})

n = 0 \sum \infty \frac{2 n + 1}{n !}

d er i v a t i v e - 2 e^{x + 2} + e^{- 5}