Question

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

Answer 1

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

Answer 2

thanks. it's been ages since i had to remember derivation rules.

Answer 3

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

Answer 4

this one involve chain rule and product rule if you like this more
there is no need for the quotient rule lol

Answer 5

since any quotient can be written as a product