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

The derivative of csc(x/2) is -cot(x/2)csc(x/2) 1/2

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

The first derivative of csc(x/2) is -cot(x/2)csc(x/2) 1/2

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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

\int \frac{cos ( x )}{4 - sin ^{2} ( x )} d x

x \to 3 lim (ln (x - 3))

x \to \infty lim (1^{+ x})

\frac{d ^{2}}{d x ^{2}} (x y)

What is the derivative of csc(x/2) ?
The derivative of csc(x/2) is -cot(x/2)csc(x/2) 1/2
What is the first derivative of csc(x/2) ?
The first derivative of csc(x/2) is -cot(x/2)csc(x/2) 1/2