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)

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\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)

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

\int \frac{( 2 + x )}{4 - 2 x - x ^{2}} d x

\int (sin (y) + y sin (x) + \frac{1}{x}) d x

\frac{d}{d x} (x^{2} \cdot x)

\frac{s}{( s - 3 ) ( s - 6 ) ( s - 2 )}

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)