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

The derivative of arctan(1+x^2) is (2x)/(x^4+2x^2+2)

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

The first derivative of arctan(1+x^2) is (2x)/(x^4+2x^2+2)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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