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

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

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

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

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

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

Solution steps

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

Simplify

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

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

\frac{d ^{2}}{d x ^{2}} (x^{5})

x \to 0 lim (0^{x})

\frac{d i}{d t}

\int \frac{1 - x}{1 - x} d x

(- x + 2) y^{^{'}} - y = e^{- 2 x}

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