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

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

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

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

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derivative of

y = \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))

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

\frac{d}{d x} (\frac{- x e ^{- x} + e ^{- x}}{e ^{x}})

n = 0 \sum \infty \frac{n + 1}{e ^{n}}

\int (1 - x^{2})^{2} d x

3 6 x^{4} + 7 x^{3}

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