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

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Answer 1 · 2017-02-27T00:00:23

$d/dx(arctan(x)/(1+x^2))=(1-2xarctan(x))/(1+x^2)^2$

The quotient rule states that the derivative of a function $f(x)=g(x)/(h(x))$ is:

$f'(x)=(g'(x)h(x)-g(x)h'(x))/(h(x))^2$

Here we see that:

Then:

$d/dx(arctan(x)/(1+x^2))=((1/(1+x^2))(1+x^2)-arctan(x)(2x))/(1+x^2)^2$

$color(white)(d/dx(arctan(x)/(1+x^2)))=(1-2xarctan(x))/(1+x^2)^2$

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