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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x, g = csc (x)

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

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

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

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

Simplify

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

\frac{b ( - 12 b - 290 )}{8 - b}

\int cos (\frac{nπ x}{3}) d x

(x^{2} + 1) d x + \frac{d y}{y} = 0, y (- 1) = 1

\frac{( 3 + 2 x )}{( 1 + x )}

\int cos^{2} (θ) sin (θ) d θ

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