What is the derivative of arctan(2t) ?

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

What is the first derivative of arctan(2t) ?

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

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derivative of

arctan (2 t)

\frac{2}{4 t ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{2}{4 t ^{2} + 1}

\frac{d}{d x} (ln (24 x))

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