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

The derivative of x/(csc(x)) is sin(x)+xcos(x)

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

The first derivative of x/(csc(x)) is sin(x)+xcos(x)

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

sin (x) + x cos (x)

Solution steps

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

Simplify

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

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

Apply the Product Rule:

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

f = x, g = sin (x)

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

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

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

= 1 \cdot sin (x) + cos (x) x

Simplify

= sin (x) + x cos (x)

What is the derivative of x/(csc(x)) ?
The derivative of x/(csc(x)) is sin(x)+xcos(x)
What is the first derivative of x/(csc(x)) ?
The first derivative of x/(csc(x)) is sin(x)+xcos(x)