What is the d/(dt)(arctan(t/2)) ?

The d/(dt)(arctan(t/2)) is 2/(t^2+4)

What is the first d/(dt)(arctan(t/2)) ?

The first d/(dt)(arctan(t/2)) is 2/(t^2+4)

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

\frac{2}{t ^{2} + 4}

Solution steps

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

Apply the chain rule:

\frac{1}{( \frac{t}{2} ) ^{2} + 1} \frac{d}{d t} (\frac{t}{2})

= \frac{1}{( \frac{t}{2} ) ^{2} + 1} \frac{d}{d t} (\frac{t}{2})

\frac{d}{d t} (\frac{t}{2}) = \frac{1}{2}

= \frac{1}{( \frac{t}{2} ) ^{2} + 1} \cdot \frac{1}{2}

Simplify

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

= \frac{2}{t ^{2} + 4}

What is the d/(dt)(arctan(t/2)) ?
The d/(dt)(arctan(t/2)) is 2/(t^2+4)
What is the first d/(dt)(arctan(t/2)) ?
The first d/(dt)(arctan(t/2)) is 2/(t^2+4)