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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of (2x)/(x^2-4x+13)

\int \frac{2 x}{x ^{2} - 4 x + 13} d x

derivative of xe^xcot(x)

\frac{d}{d x} (x e^{x} cot (x))

derivative of-10x+3cos(x)

\frac{d}{d x} (- 10 x + 3 cos (x))

derivative of (6x/(x+5))

\frac{d}{d x} (\frac{6 x}{x + 5})

integral of e^{-5x}cos(3x)

\int e^{- 5 x} cos (3 x) d x