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How do you find the derivative of #(X/(X^2+1))#?

1 Answer

Shwetank Mauria

Jul 4, 2016

#(df)/(dx)=(1-x^2)/(x^2+1)^2#

Explanation:

As #f(x)=x/(x^2+1)#, using quotient rule,

#(df)/(dx)=(d/(dx)x xx (x^2+1)-d/(dx)(x^2+1)xx x)/(x^2+1)^2#

= #(1xx(x^2+1)-2x xx x)/(x^2+1)^2#

= #(1-x^2)/(x^2+1)^2#

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