What is the derivative of sqrt(csc(2x)) ?

The derivative of sqrt(csc(2x)) is -cot(2x)sqrt(csc(2x))

What is the first derivative of sqrt(csc(2x)) ?

The first derivative of sqrt(csc(2x)) is -cot(2x)sqrt(csc(2x))

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

- cot (2 x) csc (2 x)

Solution steps

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

Apply the chain rule:

\frac{1}{2 csc ( 2 x )} \frac{d}{d x} (csc (2 x))

= \frac{1}{2 csc ( 2 x )} \frac{d}{d x} (csc (2 x))

\frac{d}{d x} (csc (2 x)) = - cot (2 x) csc (2 x) \cdot 2

= \frac{1}{2 csc ( 2 x )} (- cot (2 x) csc (2 x) \cdot 2)

Simplify

\frac{1}{2 csc ( 2 x )} (- cot (2 x) csc (2 x) \cdot 2) : - cot (2 x) csc (2 x)

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

What is the derivative of sqrt(csc(2x)) ?
The derivative of sqrt(csc(2x)) is -cot(2x)sqrt(csc(2x))
What is the first derivative of sqrt(csc(2x)) ?
The first derivative of sqrt(csc(2x)) is -cot(2x)sqrt(csc(2x))