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

1 Answer
Andrea S.
Oct 6, 2017

#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#

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