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

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

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

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

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

- \frac{cot ( x ) csc ( x )}{2}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int 15 cos (15 x) d x

f (x) = 9 x - 10 x^{\frac{1}{4}}

\int \frac{1}{cos ( y )} d y

\int_{0}^{0.75} 2 x d x

\frac{d}{d x} (A x^{- \frac{1}{2}})

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