What is the derivative of ln(arctan(x)) ?

The derivative of ln(arctan(x)) is 1/(arctan(x)(x^2+1))

What is the first derivative of ln(arctan(x)) ?

The first derivative of ln(arctan(x)) is 1/(arctan(x)(x^2+1))

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derivative of

ln (arctan (x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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