derivative of (cos(2x)/(sin(x)))

Lösung

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

- 2 sin (2 x) csc (x) - cot (x) csc (x) cos (2 x)

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Produktregel an:

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

f = cos (2 x), g = csc (x)

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

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

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

= (- sin (2 x) \cdot 2) csc (x) + (- cot (x) csc (x)) cos (2 x)

Vereinfache

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

\int_{1}^{2} \frac{x}{x ^{2} + 4 x + 20} d x

\int_{0}^{0.4} \frac{( x ^{2} )}{4 - 25 x ^{2}} d x

\frac{\partial}{\partial x} (y x - y - x)

y^{^{'}} = 5 x - y

\frac{d}{d x} (x y^{2} - x^{3} y)