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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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