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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the common derivative:

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

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

Simplify

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

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