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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 2 \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}

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

Simplify

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

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

y^{^{'}} = x^{2} - y

36 y^{^{''}} - y = x e^{\frac{x}{6}}, y (0) = 1, y^{^{'}} (0) = 0

f^{^{'}} (x) = 1

\int 64 x d x

2 x^{3} + 8 x^{2} - 5 x + 9

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