What is the derivative of (cos(2x)/(sin(x))) ?

The derivative of (cos(2x)/(sin(x))) is -2sin(2x)csc(x)-cot(x)csc(x)cos(2x)

What is the first derivative of (cos(2x)/(sin(x))) ?

The first derivative of (cos(2x)/(sin(x))) is -2sin(2x)csc(x)-cot(x)csc(x)cos(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

(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)

Simplify

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

What is the derivative of (cos(2x)/(sin(x))) ?
The derivative of (cos(2x)/(sin(x))) is -2sin(2x)csc(x)-cot(x)csc(x)cos(2x)
What is the first derivative of (cos(2x)/(sin(x))) ?
The first derivative of (cos(2x)/(sin(x))) is -2sin(2x)csc(x)-cot(x)csc(x)cos(2x)