find the derivative of x/((x^2)+1)

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find the derivative of x/((x^2)+1)

Mathematics
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f'(x)=[(derivativetop)(bottom)-(deritiavebottom)(top)]/(bottom)^2 =[(1)(x^2+1)-(2x)(x)](x^2+1)^2 =(x^2+1-2x^2)/(x^2+1)^2 =(-x^2+1)/(x^2+1)^2
thanks. it's been ages since i had to remember derivation rules.
np you can also rewrite f(x) and not use the quotient rule f(x)=x(x^2+1)^(-1) f'(x)=1(x^2+1)^(-1)+x(-1)(2x)(x^2+1)^(-2) =1/(x^2+1)-2x^2/(x^2+1)^2 =[(x^2+1)-2x^2]/(x^2+1)^2 =(-x^2+1)/(x^2+1)^2

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Other answers:

this one involve chain rule and product rule if you like this more there is no need for the quotient rule lol
since any quotient can be written as a product

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