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Beliebt Rechnen >

derivative of 1/(csc^2(x))

Lösung

\frac{d}{d x} (\frac{1}{csc ^{2} ( x )})

Lösung

sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{csc ^{2} ( x )})

Vereinfache

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

= \frac{d}{d x} (sin^{2} (x))

Wende die Kettenregel an:

2 sin (x) \frac{d}{d x} (sin (x))

= 2 sin (x) \frac{d}{d x} (sin (x))

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

= 2 sin (x) cos (x)

Verwende die Doppelwinkelidentität:

2 sin (x) cos (x) = sin (2 x)

= sin (2 x)

Graph

Beliebte Beispiele

(dy}{dx}=-\frac{5x)/y

\frac{d y}{d x} = - \frac{5 x}{y}

derivative of e^{tan(2x+1})

\frac{d}{d x} (e^{t a n (2 x + 1)})

limit as x approaches 5-of |x-5|

x \to 5 - lim (∣ x - 5 ∣)

integral of-cos(x)+sin(x)+2

\int - cos (x) + sin (x) + 2 d x

derivative of sqrt(-5x+5)

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