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Beliebt Rechnen >

derivative 1/(sin^2(x))

Lösung

ableitung von

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

Lösung

- 2 csc^{2} (x) cot (x)

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 2 csc (x) (- cot (x) csc (x))

Vereinfache

2 csc (x) (- cot (x) csc (x)) : - 2 csc^{2} (x) cot (x)

= - 2 csc^{2} (x) cot (x)

Graph

Beliebte Beispiele

integral of x^2sqrt(9+x)

\int x^{2} 9 + x d x

steigung x/(x^2+1)

s l o p e \frac{x}{x ^{2} + 1}

(x^2+1)(dy)/(dx)+6x(y-1)=0,y(0)=8

(x^{2} + 1) \frac{d y}{d x} + 6 x (y - 1) = 0, y (0) = 8

integral of (x+6)^4

\int (x + 6)^{4} d x

fläche y=x,y=sqrt(x),x=0,x=2

a re a y = x, y = x, x = 0, x = 2