derivative of 7arctanh(cos(x))

Lösung

\frac{d}{d x} (7 arctanh (cos (x)))

- 7 csc (x)

Schritte zur Lösung

\frac{d}{d x} (7 arctanh (cos (x)))

Entferne die Konstante:

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

= 7 \frac{d}{d x} (arctanh (cos (x)))

Wende die Kettenregel an:

\frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

= \frac{1}{1 - ( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

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

= 7 \cdot \frac{1}{1 - ( cos ( x ) ) ^{2}} (- sin (x))

Vereinfache

7 \cdot \frac{1}{1 - cos ^{2} ( x )} (- sin (x)) : - 7 csc (x)

= - 7 csc (x)

x \to 2 lim (\frac{x ^{4} - 16}{x ^{3} - 8})

\int e^{2 x} - 1 d x

\int \frac{5 x ^{2}}{( 121 + x ^{2} ) ^{2}} d x

x \to 1 lim (\frac{1}{ln ( x )})

\int 7 e^{x} - 3 d x