derivative of x/(sin(2x))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

f = x, g = csc (2 x)

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

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

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

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

Vereinfache

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

\int 3 x^{2} - 18 x + 27 d x

\frac{d}{d x} (\frac{1}{x ^{7}})

in v erse l a pl a ce \frac{4 s}{s ^{2} + 8 s + 20}

\frac{d}{d x} ((3 x^{2} - 6 x - sin (x))^{4})

\int_{x}^{2} 1 d x