What is the derivative of arctan(2y) ?

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

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

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

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derivative of

arctan (2 y)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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