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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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