Question

What's the derivative of `arctan(x)/(1+x^2)`?

Answer 1

`d/dx ( arctanx/(1+x^2) ) = ( 1- 2xarctanx )/(1+x^2)^2`

Explanation:

Using the quotient rule:

`d/dx (f/g) = (g * (df)/dx - f * (dg)/dx)/g^2`

we have:

`d/dx ( arctanx/(1+x^2) ) = ( (1+x^2) d/dx arctanx - arctanx d/dx (1+x^2))/(1+x^2)^2`

`d/dx ( arctanx/(1+x^2) ) = ( (1+x^2)(1/(1+x^2)) -2x arctanx )/(1+x^2)^2`

`d/dx ( arctanx/(1+x^2) ) = ( 1- 2xarctanx )/(1+x^2)^2`