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

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Jun 7, 2015

Renaming #u=1+x^2#, we can use the chain rule, which states that #(dy)/(dx)=(dy)/(du)(du)/(dx)#

Also, we can rewrite #1/u# as #u^-1#, following the rule of negative exponentials: #a^-n=1/a^n#

#(dy)/(dx)=-u^-2(2x)#

Substituting #u#:

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

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