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Beliebt Rechnen >

derivative of csc^3(2x)

Lösung

\frac{d}{d x} (csc^{3} (2 x))

Lösung

- 6 csc^{3} (2 x) cot (2 x)

Schritte zur Lösung

\frac{d}{d x} (csc^{3} (2 x))

Wende die Kettenregel an:

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

= 3 (csc (2 x))^{2} \frac{d}{d x} (csc (2 x))

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= 3 (csc (2 x))^{2} (- cot (2 x) csc (2 x) \cdot 2)

Vereinfache

3 csc^{2} (2 x) (- cot (2 x) csc (2 x) \cdot 2) : - 6 csc^{3} (2 x) cot (2 x)

= - 6 csc^{3} (2 x) cot (2 x)

Graph

Beliebte Beispiele

tangent x^4-20x^2+64

t an g e n t x^{4} - 20 x^{2} + 64

derivative of x^5y

\frac{d}{d x} (x^{5} y)

integral of (cos(x))/(4+sin(x))

\int \frac{cos ( x )}{4 + sin ( x )} d x

integral of (2-5x)/(x^6)

\int \frac{2 - 5 x}{x ^{6}} d x

(dy)/(dx)+(2xy)/(x^2+1)=x

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