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

The derivative of arccot(x/2) is -2/(x^2+4)

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

The first derivative of arccot(x/2) is -2/(x^2+4)

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

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

Solution steps

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

Apply the chain rule:

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

= - \frac{1}{( \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} + 1} \cdot \frac{1}{2}

Simplify

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

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

f (x) = 7 - x^{2}

\int_{0}^{20} 1

\int 5 x^{2} sin (π x) d x

\frac{d}{d x} (ln ∣ x + 1 ∣)

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

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