Question

differentiate f(x)=x/(1+x^2)

Answer 1

\[
f'(x)=\frac {1+x^2 -2 x x}{(1+x^2)^2}=\frac {1-x^2}{(1+x^2)^2}
\]

Answer 2

Apply quotient's rule.

Answer 3

could you show me how?

Answer 4

\[

\frac{u'v - v'u }{v^2}

\]

Answer 5

\[ u= x\\
v=1+x^2

\]

Answer 6

\[
u'=1\\
v'= 2 x

\]

Answer 7

Can you take it from here?

Answer 8

ahh yes i have figured it out :) thank you :) do you know if there a trick for knowing what rule to use?

Answer 9

if it's a quotient, use quotient rule.
If it's product, us product's rule