What is the (2arctan(t))^' ?

The (2arctan(t))^' is 2/(t^2+1)

What is the first (2arctan(t))^' ?

The first (2arctan(t))^' is 2/(t^2+1)

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(2 arctan (t))^{^{'}}

\frac{2}{t ^{2} + 1}

Solution steps

(2 arctan (t))^{'}

Take the constant out:

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

= 2 (arctan (t))^{^{'}}

Apply the common derivative:

(arctan (t))^{'} = \frac{1}{t ^{2} + 1}

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

Simplify

2 \cdot \frac{1}{t ^{2} + 1} : \frac{2}{t ^{2} + 1}

= \frac{2}{t ^{2} + 1}