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Beliebt Rechnen >

derivative h(x)=(2x)/(sin(x))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = csc (x)

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

\frac{d x}{d x} = 1

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

= 2 (1 \cdot csc (x) + (- cot (x) csc (x)) x)

Vereinfache

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

Graph

Beliebte Beispiele

derivative of (x^2+x(6-x))

\frac{d}{d x} ((x^{2} + x) (6 - x))

integral of 1/(sqrt(7x+6))

\int \frac{1}{7 x + 6} d x

slopeintercept (2,4),(5,13)

s l o p e in t erce pt (2, 4), (5, 13)

integral of (1/3)^x

\int (\frac{1}{3})^{x} d x

limit as x approaches 4 of x/(x+1)

x \to 4 lim (\frac{x}{x + 1})