What is (\partial)/(\partial x)(arctan(2x)) ?

The answer to (\partial)/(\partial x)(arctan(2x)) is 2/(4x^2+1)

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(\partial)/(\partial x)(arctan(2x))

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{( 2 x ) ^{2} + 1} \frac{\partial}{\partial x} (2 x)

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

\frac{\partial}{\partial x} (2 x) = 2

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

Simplify

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

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

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What is (\partial)/(\partial x)(arctan(2x)) ?
The answer to (\partial)/(\partial x)(arctan(2x)) is 2/(4x^2+1)