Question

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

Answer 1

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`