What is the derivative of ln(arctan(x+1)) ?

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

What is the first derivative of ln(arctan(x+1)) ?

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

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derivative of

ln (arctan (x + 1))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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