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Popular >

derivative of ln(arctan(2x))

Solution

\frac{d}{d x} (ln (arctan (2 x)))

Solution

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

Solution steps

\frac{d}{d x} (ln (arctan (2 x)))

Apply the chain rule:

\frac{1}{arctan ( 2 x )} \frac{d}{d x} (arctan (2 x))

= \frac{1}{arctan ( 2 x )} \frac{d}{d x} (arctan (2 x))

\frac{d}{d x} (arctan (2 x)) = \frac{2}{4 x ^{2} + 1}

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

Simplify

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

= \frac{2}{arctan ( 2 x ) ( 4 x ^{2} + 1 )}

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Frequently Asked Questions (FAQ)

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