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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Apply the Product Rule:

(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

Simplify

= 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}})

\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

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