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

The derivative of sqrt(arctan(x/2)) is 1/(sqrt(arctan(x/2))(x^2+4))

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

The first derivative of sqrt(arctan(x/2)) is 1/(sqrt(arctan(x/2))(x^2+4))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (\frac{x}{2})) = \frac{2}{x ^{2} + 4}

= \frac{1}{2 arctan ( \frac{x}{2} )} \cdot \frac{2}{x ^{2} + 4}

Simplify

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

= \frac{1}{arctan ( \frac{x}{2} ) ( x ^{2} + 4 )}

What is the derivative of sqrt(arctan(x/2)) ?
The derivative of sqrt(arctan(x/2)) is 1/(sqrt(arctan(x/2))(x^2+4))
What is the first derivative of sqrt(arctan(x/2)) ?
The first derivative of sqrt(arctan(x/2)) is 1/(sqrt(arctan(x/2))(x^2+4))