derivative of ln(1/(cos(x)))

Lösung

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

tan (x)

Schritte zur Lösung

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

Vereinfache

ln (\frac{1}{cos ( x )}) : ln (sec (x))

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

= \frac{1}{sec ( x )} sec (x) tan (x)

Vereinfache

\frac{1}{sec ( x )} sec (x) tan (x) : tan (x)

= tan (x)

x \to a lim (\frac{0}{0})

\frac{\partial}{\partial x} (x e^{6 x y})

\int_{0}^{\infty} \frac{2}{x ^{2} + 4} d x

y^{2} \frac{d y}{d x} = 1

\int x arctan (20 x) d x