What is the derivative of 4cot(x/8) ?

The derivative of 4cot(x/8) is -1/2 csc^2(x/8)

What is the first derivative of 4cot(x/8) ?

The first derivative of 4cot(x/8) is -1/2 csc^2(x/8)

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\frac{d}{d x} (4 cot (\frac{x}{8}))

- \frac{1}{2} csc^{2} (\frac{x}{8})

Solution steps

\frac{d}{d x} (4 cot (\frac{x}{8}))

Take the constant out:

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

= 4 \frac{d}{d x} (cot (\frac{x}{8}))

Apply the chain rule:

- csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

= - csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= 4 (- csc^{2} (\frac{x}{8}) \frac{1}{8})

Simplify

4 (- csc^{2} (\frac{x}{8}) \frac{1}{8}) : - \frac{1}{2} csc^{2} (\frac{x}{8})

= - \frac{1}{2} csc^{2} (\frac{x}{8})

0.5

\int (x^{6} + \frac{1}{1 - 4 x ^{2}}) d x

\int_{8}^{\infty} \frac{1}{x ^{2} + x} d x

y^{^{'}} = (y + 4 x)^{2}

x \to 1 + lim (\frac{x ^{2}}{x ^{2} - 1})

What is the derivative of 4cot(x/8) ?
The derivative of 4cot(x/8) is -1/2 csc^2(x/8)
What is the first derivative of 4cot(x/8) ?
The first derivative of 4cot(x/8) is -1/2 csc^2(x/8)