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

The derivative of arccsc(x/2) is -2/(xsqrt(x^2-4))

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

The first derivative of arccsc(x/2) is -2/(xsqrt(x^2-4))

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

- \frac{2}{x x ^{2} - 4}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{( \frac{x}{2} ) ^{2} ( \frac{x}{2} ) ^{2} - 1} \cdot \frac{1}{2} : - \frac{2}{x x ^{2} - 4}

= - \frac{2}{x x ^{2} - 4}

What is the derivative of arccsc(x/2) ?
The derivative of arccsc(x/2) is -2/(xsqrt(x^2-4))
What is the first derivative of arccsc(x/2) ?
The first derivative of arccsc(x/2) is -2/(xsqrt(x^2-4))