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

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

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

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

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

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

Solution steps

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

Simplify

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

= \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)

= \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)

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

Simplify

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

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